The java web app works fine with fresh tomcat recycle. After working for sometime, it hangs. No logs or exception appear at all. A tomcat recycle again brings back the web app to working state.
What is the best way to debug this problem? Are there any specific tools to analyze such kind of hung behavior?
You could try running VisualVM. Have it hook onto the Tomcat instance and have it show you exactly what's happening.
More info:
Monitoring Tomcat with Java VisualVM
Have you tried the Tomcat Manager/Status app? You can visit them by http://host:port/ without the name of your app. Did you find anything interesting there? You will need to figure out the Tomcat has problems or your app has problems first.