Tomcat stops responding after a few days without crashing

I have a release issue where tomcat becomes unresponsive after a few days.
Below are my observations:

• The tomcat application was under constant load.
• Dedicated heap - 1024 MB and 512 MB PermGen
• Tomcat processes consumed 2.75 GB of memory.
• The total memory (machine) is 4GB, and the other process also works like jmxTranse and other monitoring tools, so the total memory consumed by all processes is 3656mb out of the total memory 3764mb.
• We also use calls to our library on the server.

My questions:

• How to debug the actual reason for tomcat hangs?
• How to debug if memory consumption is caused by subscriber calls?

Please let me know if the heap state needs to be posted.