cPanel Intermittent network problem

Hello guys,

I work in an organization that offer web hosting services to multiple customers in my country.We currently have cPanel server running on CentOS 5.3 which has been working perfectly for close to two years now. Recently, we stated having outage issues on the cPanel server.
Here is the nature of the problem:
We have observed that the server normally time out anytime between 12:00am and 8:00am every day.
We have looked into the log files but nothing seems to point to the root cause of the problem. It has gotten to the extent that customers are actually the ones that do inform us of service outage. In order to salvage this problem, what we normally do is to do a system restart which do solve the problem.
Kindly come to my aid as I normally do restart of my server on a daily basis which is giving me a lot of concerns.

Thanks for your professional anticipated assistance.