I'm seeing the same problem with my AEON Z-stick Gen 5 on a RPi B+ running jessie. This has been happening for several days with r512 and the (log/homegenie.log) doesn't help since the last few lines aren't flushed. The symptoms are exactly the same as mblack described earlier and restarting the service, either from the HG web UI or using systemctl restart, fixes the problem for the next 12 hours or so.
Upgrading the default version of Mono on the RPi from 3.2 to 4.0 didn't help, although it seems to be more stable. I used to see errors in the log file approximately like "object used after being disposed" which went away with the upgrade.
I tried r513 RC from the "testing" area on SourceForge and it suffers from the same malady. I even built HG from the sources at GitHub (from the head) with no relief. I suspect the problem is in one of the libraries, possibly ZWaveLib.dll, which are not rebuilt when HG is. Maybe I should try rebuilding everything.
The other thing that comes to mind is that SolarAltitude updates the scheduler every 12 hours. And I rely on it quite heavily for turning lights on/off. I wonder if the 12 hours is a coincidence??
By the way, all my FireCracker based X10 devices continue to work, so the problem is probably not in the HG framework code but in some low level library like MIG or ZWave.
I've attached one of the failing homegenie.log files. Hopefully some expert can shed some light.