Timeouts when I have more than 1500 sessions

Absolutely not. Perhaps it's not the F5 but a function of the real servers when they are under load? Have you checked the resource usage there when connections are high?

 

 

To be 100% I'd say a packet capture using tcpdump is in order, you can keep the captured data low by capturing data only from one test client that you connect when connections are low, just before they normally ramp up. You can capture client and server-side at the same time. Then you'd know for sure who's actually closing the connection, the F5 or the servers.