I run jstat with option <each second> redirected into a file, this will give a good picture of the memory consumption over the time.
Also it will have no big sideeffect to memory and resoures.
JProfile is not a good idea in production, the server will become very slow ~10-20% of normal performance and maybe the problem dissapear because of less load.
Memory snapshot might take a while during the dump and this might not acceptable in production.
Could you also post the JVM start parameter?
There are many reasons for such memory problems, so feel free to ask with more informations :)