Without any specific details I would guess you are running out of connections (ie connections are not always being closed correctly by the application and hence you eventually run out of available connections in your pool). As this is not happening "quickly" and takes a day to appear I would investigate areas of your code that is not triggered on a regular basis. Using a stress testing tool like jmeter to hit many different urls in your site may also give you an insight into what is happening. I doubt if this is a technical issue with GF or Hibernate (assuming you are using the latest versions of each).
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