Hi Fabrizio,
The logs you've sent us are relatively old (~2 weeks), so I assume you haven't tried to rediscover the F5 device as I've suggested in my previous post. I'd like to start a clean slate in troubleshooting your issue, so that we can make some progress towards a quick resolution. From your current logs I can only see that the F5 Monitoring Service (the actual F5 device monitoring agent) cannot communicate with the SCOM Health Service. This could have multiple reasons and I would like you to first check the following (and please post back here the results/answers):
1. The account running the F5 Monitoring Service is part of the Operations Manager Administrators group. You can verify this in the SCOM Management Console :: Administration :: Security :: User Roles :: Operations Manager Administrators :: General Properties.
2. Tell us more about your SCOM deployment: is it a single RMS or do you have multiple management servers? If you do have multiple management servers, did you first install the F5 MP on the RMS and then on the other management server(s)?
Let's start and build our troubleshooting case from here. Please email us the setup.log file, found in Program Files\F5 Networks\Management Pack\log folder.
Thank you.
Julian