address persistent allow the device to assign the same address from source pool to a specific host for multiple concurrent sessions.
The question here, For How long does the address persistent maintain the address for the host ???
This kb article gives the full definitions with examples.
address persistent exists for the length of the normal session table on the device. So when the last session closes then the address is released to the pool.
adding persistent nat puts a 600 second timer by default before the address is returned and you can configure a value on the time.