We've been experiencing some difficulty with VDI sessions terminating for unknown reasons and VMWare is stating they believe the issue to be with persistence settings on the LTM. I would like to see F5's current setup recommendations in the LTM to support VDI.
You can configure LTM to show the cause of connection reset. Once done, try to capture the logs and analyse it using wireshark. Once you are certain, you can modify the config accordingly. You also need to see different TCP timeouts that you may have configured. Generally, cookie/source/destination persistence are used, so accompanied with TCP profile config and persistence, you can optimize the session connectivity.