Questions like this are tough to answer. Issues like this need to be answered by assessing several vital variables. It goes like this when you are trying to provide an answer to how long it will take for sweatbands to saturate.
For starters, ignoring the fabrics for just a second, the ambient temperature and humidity outdoors will play a role. Additionally, the airflow and how much you sweat will also be necessary. Depending on the conditions and yourself, even some of the best models can saturate very quickly.