bug: GraphFlow with termination condition automatically ends after first query.

### What happened?

**Describe the bug**
When I run GraphFlow API and using a termination condition, it would not continue conversation without resetting team state.

**To Reproduce**
Steps to reproduce the behavior. Please include code and outputs such as stacktrace.

- If your input is just "I tried X, and it didn't work" or
"X is not working", your issue will be ignored.
- If your input is not well formatted, it will hurt readability and
may be ignored as well.

Here is the piece of code that I used to replicate the issue, mostly following the example from GraphFlow:

```python
import asyncio
import os
from autogen_agentchat.agents import (
    AssistantAgent,
    MessageFilterAgent,
    MessageFilterConfig,
    PerSourceFilter,
)
from autogen_agentchat.teams import DiGraphBuilder, GraphFlow
from autogen_agentchat.ui import Console
from autogen_ext.models.openai import OpenAIChatCompletionClient
from autogen_agentchat.conditions import TextMentionTermination
from dotenv import load_dotenv

load_dotenv()

# Model client
client = OpenAIChatCompletionClient(
    model="gpt-4.1-nano", api_key=os.getenv("OPENAI_API_KEY")
)

# Create agents
researcher = AssistantAgent(
    "researcher",
    model_client=client,
    system_message="Summarize key facts about climate change.",
)
analyst = AssistantAgent(
    "analyst",
    model_client=client,
    system_message="Review the summary and suggest improvements.",
)
presenter = AssistantAgent(
    "presenter",
    model_client=client,
    system_message="Prepare a presentation slide based on the final summary. tell TERMINATE when you are done.",
)

# Apply message filtering
filtered_analyst = MessageFilterAgent(
    name="analyst",
    wrapped_agent=analyst,
    filter=MessageFilterConfig(
        per_source=[PerSourceFilter(source="researcher", position="last", count=1)]
    ),
)

filtered_presenter = MessageFilterAgent(
    name="presenter",
    wrapped_agent=presenter,
    filter=MessageFilterConfig(
        per_source=[PerSourceFilter(source="analyst", position="last", count=1)]
    ),
)

# Build the flow
builder = DiGraphBuilder()
builder.add_node(researcher).add_node(filtered_analyst).add_node(filtered_presenter)
builder.add_edge(researcher, filtered_analyst).add_edge(
    filtered_analyst, filtered_presenter
)

# Create the flow
flow = GraphFlow(
    participants=builder.get_participants(),
    graph=builder.build(),
    termination_condition=TextMentionTermination("TERMINATE"),
)


# Run the flow
async def main():
    await Console(flow.run_stream(task="Summarize key facts about climate change."))
    await Console(flow.run_stream(task="Review the summary and suggest improvements."))


if __name__ == "__main__":
    asyncio.run(main())
```

I tried with two consecutive messages, and it doesn't execute the second query even though the first one was successful:

```bash
➜  ai git:(feat/autogen-graphflow) ✗ python example.py
---------- TextMessage (user) ----------
Summarize key facts about climate change.
---------- TextMessage (researcher) ----------
Climate change refers to long-term shifts in temperature, precipitation, and weather patterns caused primarily by human activities, especially the burning of fossil fuels, deforestation, and industrial processes. Key facts include:

1. Global warming: Earth's average surface temperature has increased by about 1.2°C (2.2°F) since the late 19th century.
2. Greenhouse gases: Elevated levels of carbon dioxide (CO₂), methane (CH₄), and nitrous oxide (N₂O) trap more heat in the atmosphere.
3. Sea level rise: Melting glaciers and expanding warmer oceans have caused sea levels to rise about 21-24 centimeters (8-9 inches) since 1880.
4. Extreme weather: Increased frequency and intensity of heatwaves, hurricanes, droughts, and heavy rainfall events.
5. Impacts on ecosystems: Threats to biodiversity, with many species at risk of extinction due to habitat loss and changing conditions.
6. Human health: Climate change affects air quality, causes heat-related illnesses, and influences the spread of vector-borne diseases.
7. Mitigation and adaptation: Strategies include reducing greenhouse gas emissions, transitioning to renewable energy, and implementing policies to adapt to changing conditions.
8. Urgency: The Intergovernmental Panel on Climate Change (IPCC) emphasizes the need to limit global warming to 1.5°C above pre-industrial levels to avoid catastrophic impacts.

Addressing climate change requires coordinated global efforts to reduce emissions and enhance resilience.
---------- TextMessage (analyst) ----------
The summary provides a comprehensive overview of climate change, covering its causes, effects, and potential solutions. To improve clarity and depth, consider the following suggestions:

1. Clarify Key Concepts: Define terms like "fossil fuels" briefly, for clarity.
2. Include Recent Data: Mention any recent developments or projections, if available, to emphasize urgency.
3. Highlight Economic and Social Impacts: Briefly note how climate change affects economies and societies.
4. Expand on Mitigation and Adaptation: Provide specific examples or policies, such as carbon pricing or reforestation efforts.
5. Emphasize Global Efforts: Mention international agreements like the Paris Agreement to contextualize solutions.
6. Enhance Flow: Organize points to improve logical flow from causes to impacts and solutions.

Revised version:

Climate change involves long-term shifts in temperature, precipitation, and weather patterns primarily resulting from human activities such as burning fossil fuels, deforestation, and industrial processes. Key facts include:

1. Global warming: Earth's average surface temperature has risen by about 1.2°C (2.2°F) since the late 19th century, leading to widespread environmental changes.
2. Greenhouse gases: Elevated levels of carbon dioxide (CO₂), methane (CH₄), and nitrous oxide (N₂O)—mainly from fossil fuel combustion and agriculture—trap more heat in the atmosphere.
3. Sea level rise: Melting glaciers and expanding seawater have caused sea levels to increase approximately 21-24 centimeters (8-9 inches) since 1880, risking coastal communities.
4. Extreme weather events: There is an increased frequency and severity of heatwaves, hurricanes, droughts, and heavy rainfall, impacting livelihoods and ecosystems.
5. Ecological impacts: Rising temperatures threaten biodiversity, with many species at risk of extinction due to habitat loss and changing environmental conditions.
6. Human health: Climate change exacerbates air pollution, causes heat-related illnesses, and facilitates the spread of vector-borne diseases like malaria and dengue.
7. Solutions: Mitigation strategies include reducing greenhouse gas emissions through renewable energy adoption, energy efficiency, and policies like carbon pricing; adaptation involves measures such as reforestation, resilient infrastructure, and sustainable agriculture.
8. Urgency and global response: The IPCC highlights the importance of limiting warming to 1.5°C above pre-industrial levels to avoid catastrophic impacts, emphasizing international efforts like the Paris Agreement to coordinate climate action.

Addressing climate change requires urgent, sustained global cooperation to cut emissions and build resilience against its impacts, safeguarding the environment and human well-being for future generations.
---------- TextMessage (presenter) ----------
- **Climate Change Overview**
  - Long-term shifts in temperature, precipitation, and weather patterns primarily due to human activities (burning fossil fuels, deforestation, industrial processes).
  
- **Key Facts & Impacts**
  - *Global Warming*: Earth's temperature has risen by ~1.2°C since late 1800s, causing environmental changes.
  - *Greenhouse Gases*: Increased CO₂, CH₄, N₂O from fossil fuel use and agriculture trap heat.
  - *Sea Level Rise*: +21-24 cm since 1880, threatening coastal communities.
  - *Extreme Weather*: More frequent heatwaves, hurricanes, droughts, heavy rains affecting lives and ecosystems.
  - *Biodiversity Loss*: Rising temperatures endanger species via habitat loss.
  - *Human Health*: Greater air pollution, heat-related illnesses, spread of diseases like malaria and dengue.
  
- **Solutions & Global Efforts**
  - *Mitigation*: Reduce emissions through renewable energy, energy efficiency, carbon pricing.
  - *Adaptation*: Reforestation, resilient infrastructure, sustainable agriculture.
  - *International Actions*: Paris Agreement to limit warming to 1.5°C and coordinate efforts.
  
- **Conclusion**
  - Urgent, sustained global cooperation is essential to cut emissions and build resilience, ensuring environmental and human well-being for future generations.

TERMINATE
---------- TextMessage (user) ----------
Review the summary and suggest improvements.
---------- StopMessage (DiGraphStopAgent) ----------
Digraph execution is complete
```


**Expected behavior**
A clear and concise description of what you expected to happen.

It should continue the conversation with state from the previous execution like SelectorGroupChat, ...
**Screenshots**
None

**Additional context**
None

### Which packages was the bug in?

Python AgentChat (autogen-agentchat>=0.4.0)

### AutoGen library version.

Python 0.6.2

### Other library version.

_No response_

### Model used

gpt-4.1-nano

### Model provider

OpenAI

### Other model provider

_No response_

### Python version

3.12

### .NET version

None

### Operating system

MacOS

Labels: needs-triage
State: closed