Hi Ivan,
What are you using for monitoring tools? If there is something that gives you database connections, that's a problem I was having with a different part of moodle, more or less the same symptom.
I still don't know what exactly caused it but what seems to have helped is putting this into my.cnf:
max_user_connections=80
I also had to pump the max_connections up quite a bit last year. But I think the max_user_connections was causing the problem in max_connections. My database connections have stabilized out at some normal levels( ~25-75 throughout the day). Previous to the max_user_connections update I would have spikes of 700+ database connections (this year on moodle 2.7, over 1000 last year on moodle 2.4), which would slow the server to a crawl.
Might or might not help depending on your particular problem, but it's a change that doesn't have a huge down side.
Also have you looked at error_log? Anything in there that might shed some light on the issue?