Subsequent, identical requests always fail

I'm having a strange issue where I try to hit either the same server or different servers twice, and the second one always gets a name-resolution failure. This *does not* happen when I use _urllib3_. This is specific to Requests, which is queer as Requests uses _urllib3_.

- This only happens on my build systems. It works as expected locally. Both local and remote are on Requests 2.9.1 .
- It happens in both Python 2.7 and Python 3. 
- It happens even when I request SSL from these servers and then get a SSL failure (because these servers aren't configured for it). Even though there is an SSL-related protocol breakdown, the first request fails properly, and the second fails due to no connection.
- Specifically, it's the `socket.getaddrinfo` call. I tested it directly.. after I due a `requests.get()`, I do a `socket.getaddrinfo()` and it fails. 
- I've tried with and without using Requests' sessions functionality. 
- I've tried requests with and without a "Connection: close" header.

The results are always identical.

```python
_LOGGER.info("SENDING REQUEST 1")

try:
    r = requests.get(url)
    r.raise_for_status()
except:
    _LOGGER.exception("There was a problem.")
else:
    raw_response = r.text

    _LOGGER.info("Response:\n=====\n{}\n=====".format(raw_response))

        
_LOGGER.info("SENDING REQUEST 2")

try:
    r = requests.get(url)
    r.raise_for_status()
except:
    _LOGGER.exception("There was a problem.")
else:
    raw_response = r.text

    _LOGGER.info("Response:\n=====\n{}\n=====".format(raw_response))
```

Output:

```
04:00:58 INFO:__main__:SENDING REQUEST 1
04:00:58 INFO:requests.packages.urllib3.connectionpool:Starting new HTTP connection (1): sanitized.url
04:00:58 DEBUG:requests.packages.urllib3.connectionpool:"GET /CiTriggerService/Notify HTTP/1.1" 405 1741
04:00:58 ERROR:__main__:There was a problem.
04:00:58 Traceback (most recent call last):
04:00:58   File "/tmp/jenkins7232109961798303504.sh", line 36, in <module>
04:00:58     r.raise_for_status()
04:00:58   File "/usr/lib/python3/dist-packages/requests/models.py", line 840, in raise_for_status
04:00:58     raise HTTPError(http_error_msg, response=self)
04:00:58 requests.exceptions.HTTPError: 405 Client Error: Method Not Allowed for url: http://sanitized.url:9091/CiTriggerService/Notify

04:00:58 INFO:__main__:SENDING REQUEST 2
04:00:58 INFO:requests.packages.urllib3.connectionpool:Starting new HTTP connection (1): sanitized.url
04:00:58 ERROR:__main__:There was a problem.
04:00:58 Traceback (most recent call last):
04:00:58   File "/usr/lib/python3/dist-packages/urllib3/connection.py", line 137, in _new_conn
04:00:58     (self.host, self.port), self.timeout, **extra_kw)
04:00:58   File "/usr/lib/python3/dist-packages/urllib3/util/connection.py", line 67, in create_connection
04:00:58     for res in socket.getaddrinfo(host, port, 0, socket.SOCK_STREAM):
04:00:58   File "/usr/lib/python3.5/socket.py", line 732, in getaddrinfo
04:00:58     for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
04:00:58 socket.gaierror: [Errno -2] Name or service not known
```

Yet, _urllib3_ works fine:

```python
import urllib3
http = urllib3.PoolManager()

print('')
print("Request 1:")
print('')

r = http.request('GET', 'http://sanitized.url:9091/CiTriggerService/Notify')
print(r.status)
print(r.data)

http = urllib3.PoolManager()

print('')
print("Request 2:")
print('')

r = http.request('GET', 'http://sanitized.url:9091/CiTriggerService/Notify')
print(r.status)
print(r.data)
```

Output:

```
04:12:52 
04:12:52 Request 1:
04:12:52 
04:12:52 405
04:12:52 b'\xef\xbb\xbf<?xml version="1.0" encoding="utf-8"?>\r\n<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-
...
04:12:52 
04:12:52 Request 2:
04:12:52 
04:12:52 405
04:12:52 b'\xef\xbb\xbf<?xml version="1.0" encoding="utf-8"?>\r\n<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-
...
```

I realize that the version that we're running on is quite a bit behind, but, given that it works perfectly fine on my local system at the same version, I doubt that an update would not make a difference and I can't blindly move forward on tweaking our provisioning process without a reason.

Closing this. Since there's no way to publicly debug this and the parameters and issue, in general are irrational and nonsensical, I'm not expecting anyone to be able to [effectively] help.