How much RAM does the server have allocated to it?
If it runs out of memory it will tend to lock up, and the watchdog sees it as a crash and stops the server.
EDIT: The vanilla server will run the best with 2 GB or more set off for it, and with your specs it might be best just to use a separate machine. (Unless of course you don't have one)
The 1.8-1.12 (as well as most servers beyond 1.6-ish) server uses too much RAM for 1GB allocation to suffice, try increasing it
Jtrent: it is most certainly NOT normal. It's not a watchdog process "OK" message. The server is overloaded.
EDIT 2: It might also be a CPU issue. If that's the case there's really no fix besides hosting it on a separate PC