MySql Connections are getting closed when we check it through Mysql but the connection opened are not getting reused and c3p0 is creating new connections all the time. If any one has idea that what thing I am missing with the configuration. Please suggest

When we check the threads state in java then it says all the thread created by c3p0 are TIMED_WAITING.

I guess, that when the connection are not getting reused , it depends exclusively on how you use hibernate, not on how you configured c3p0 settings.
If you use stateful contexts (transaction scopes), then a connection is only put back to pool for re-usage when you call session.close (entityManager.close with JPA approach). Do you call session close at all ?

N.B.: I used c3p0 for more than a year in our production environment and never had such behaviour you describe.