Right, it's just a development lab. However I am able to reproduce the problem every time I install new servers. Symptoms are always the same. Server runs fine, then with no apparent reason, IIS AppPools start crashing with a System.NullReference exception. Managed Availabilty probes create a loop: AppPools are restarted, then crash again when probes activity occur. Stopping and disabling the MSExchangeHM and MSExchangeHMRecovery stopped the crashes. Strangely, RemotePS was affected too. While ti was working fine initially, I suddenly could no longer use the RPS web service, however proxying (using the TargetServer Uri param) through another (unaffected) server worked fine. This leads to think that only the CAFE is affected. With MSExchangeHM disabled, and after a couple restarts, RemotePS was back. No idea why this is happening, Servers are running in Hyper-V 2012 R2 and are largely under-sized (again it's a dev lab). However I have others servers of the same size (and same host/disks/etc) on Win 2012 R2 and they run normally.
Strange...
PS: I'm not asking for any kind of support here, only passing out some info... :)