The following alerts about handle counts are raised:
"Health Service (Monitoring Host) Handle Count has exceeded the threshold" or "Health Service Handle Count has exceeded the threshold" on collector server.
The monitors raising the mentioned alerts ensure that the "Process\Handle Count" counter for the "MonitoringHost.exe" and "HealthService.exe" processes does not exceed a specific threshold over a series of consecutive samples. If the conditions are met, this monitor will change to a critical state, which will then roll up to the "Health Service State" monitor.
In the Veeam MP case, the values that trigger the monitor may result from Collector server overload. If too many VMware hosts and VMs are monitored, then the Health Service may be overwhelmed when processing the data.
Current amount of handle counts can be checked using Windows Task Manager on the collector server:
1) Start Windows Task Manager and switch to the Processes tab
2) Choose View -> Select columns and enable Handles
After that you should be able to see a column named "Handles"
Please check configuration of SCOM Agent co-located with Veeam collector (see KB1026), make sure you don't have "Veeam Collector: Health Service dropped data" or "Veeam Collector: Health Service workflows failed" alerts raised (KB1765).
If no additional alerts indicating performance issues with SCOM Agent occur, you can try increasing thresholds for 2 monitors based on current number of handles:
1) MonitoringHosts.exe "Veeam Collector: Health Service (Monitoring Host) Handle Count threshold"
2) HealthService.exe "Veeam Collector: Health Service Handle Count threshold"
Otherwise you may consider moving VMware monitoring jobs to other Veeam Collectors or co-locating Veeam Collector with a SCOM Management Server.