gradually creeps up and up eventually exceeding the physical memory (2GB)
sounds like a memory leak to me.
Search the web, on how to check your system if some apps are leaking (but do it mannualy, don't download some software that promises to detect this). Could be a memory leak from some cheap software or apps that are coded by some lousy programmers.
You're using a software that's badly coded and could compromise your safety as it will overwrite your system memory.
hope this helps