Hi Srihari,
This is one of the known issue with QC 11 (with earlier patches). HP fixed this issue in patch 10 or higher (I believe). This issue occurs when heap size reachs maximum space as mentioned in error. restarting the server resolves this issue.
This error can occur if more no. of users are connected to QC, if people are running QC excel reports involving large queries (which can result in memory leak), QC sense consumes memory, also the java process related to QC running on server consumes increasingly more memory as time passes.
You can follow some steps to avoid this issue in future:
1) Try considering QC Sense Off if you are not using it. Admin guide explains how to turn it off
2) Increase your heap space currently allocated to QC Application. QC Install guide explains how to do this
3) Try to schedule a job to restart your QC server once/twice every week (like saturday night when no body is using it).
4) Monitor QC debug page (qcbin/debug) to keep a track on the space available, processes/jobs running, any unwanted queries running.
Earlier, this outage used to happen for us every alternate day (when we were on patch 6). restarting the server was only solution that time. After that, I followed the above steps in my QC environment to minimize this issue.
Also try reconsidering to upgrade to latest patch (patch 17) which can provide some stability to QC env.