This behavior is triggered based on a setting in the Extensions > Call Queue > Agent Settings:
If an agent fails to answer more than the Max No Answer the agent is automatically put into a status of being On Break and the system will stop sending calls to that agent.
When the agent is ready to log back into the queue they can join the queue again by clicking Login on the Queue Dashboard or by pressing *10 on their phone to join the queue again.
Does the Max No Answer count increase if the agent is on DND?
DND overrides this counter and puts the agent directly into On Break status.
How does the Max No Answer count reset?
The Max No Answer count is based on an agents session which is restarted when they log into a queue and ends when they log out of a queue. This means if the agent forgets to log out of the queue at the end of a shift, and they miss 10 phone calls over night when they come back their phone will likely be on break.
Is there a max that value can be set to or a way to disable it?
You can set the number to a very large number 100 or 1000 to pretty much disable the behavior.