F5 URL is not working.

As per logs its looks like API Webservice client call waited for longer time for the server response and throws Timeout error once it reached the time limit.

You can try some other option from load balancer(

Hit and trial method

a) Increase TCP timeout and enable SNAT automap

b) If more then one pool member in pool then keep one online & rest force offline.

For Time being remove cookie persistent and clear cookie session table

c) Run the TCPdump and see the packet flow.

b) Bypass the load balancer and directly reach to server and see the difference.