Sporadic database connection issue

[eluser]GridWave[/eluser]
Hey All,

On our production server, which gets quite a few visits, there is a problem where, at times, we get cannot connect to database. I have upped the my.cnf files thresholds for the number of connections and such but we continue to get this error. The resources on the server are not being pushed to the extreme, so that isn't it either.

The error:
An Error was Encountered
Unable to connect to your database server using the provided settings

(the generic CI error)

Has anyone run into this problem before or have ideas on how we can tweak in order to stop this?

Thank you for your time and help,
Gridwave