f5 LTM, Time out issue.

you need to take a packet capture including timeout scenario: 

tcpdump -vvnni 0.0:nnnp host <Client_IP> -s0 -vw /var/tmp/TEST.pcap

Also, answer on those Questions: 
 
- The app works fine if you disable each of Nodes separately or you disable the same node each time ? 

- what is the service port on your nodes is it ( 9080 ) ? Is it the same port for both of nodes ? 

- Try to change load balancing method and see the result. 

_ what about the health monitor status in your nodes/pool members ? 

But Again the Packet capture is the most effective troubleshooting step to be taken in your scenario. 

thanks