I'd agree with sloddl, the VPS hasn't got enough memory, one of your scrpts start using all the memory and VPS starts swapping.

Next thing is, you get a lot of visitors, a lot of (I'm guessing you're using Apache) web server processes are spawned to suffice the demand and it starts eating all of your memory.

The server should be monitored to check what is the cause of this behavior, the soulution can't be found out of the blue for such server behavior.

Can you tell me how much RAM/swap have you got, kind of setup you are running and amount of daily visitors ?

If you're not getting a high hourly/daily visitor count, then you have a script that keeps hogging up the RAM..