Site is not working, with "503 Service Unavailable" error.
Plesk installed inside Virtuozzo container.
Some random applications inside container could produce "access denied" errors.
Container's limit of processes was reached. Hence some random processes inside container were killed.
Check current quantity of processes and limit of processes:
Run command on hardware node:
C:\>vzlist -o numproc,numproc.b <CTID> NPROC NPROC.B 75 80
If the limit is almost reached, increase it:
C:\>vzctl set <CTID> --numproc 150 Command 'set' is successfully finished
Restart site application pool in IIS.