You're using a Virtuozzo instance, which isn't really a VPS but a container, basically a kernel enforced chroot. From what I've seen from my dealing with it, its OOM manager is very dodgy. Because of the way it works, another container on the same hardware node could be hogging memory, but because your processes started after the processes causing the issue, your processes get killed.
Unfortunately you can only see what the OOM is upto on the host server, so you'll have to check this with your provider. Most likely they've oversold the memory on the server you're on a bit more than they should.
To quote the Linux Memory Manager page:
So the ideal candidate for liquidation is a recently started, non privileged process which together with its children uses lots of memory, has been nice'd, and does no raw I/O. Something like a nohup'd parallel kernel build (which is not a bad choice since all results are saved to disk and very little work is lost when a 'make' is terminated).
My theory is that Virtuozzo hasn't touched the OOM manager in the host kernel to make it aware that there's virtualised processes running, so it doesn't realise it's killing privileged processes in your "VPS". However, that's just conjecture as I haven't been able to check it with Parallels, who're the people responsible for Virtuozzo.