If you have SQL error logging turned on then you should be able to get more info in the logs via the Control Panel.
My guess is it's going to be one of two things since you said it resolves itself. Either max_connections are being met and it won't allow for any new ones during the time you're trying to access, or your host as a max queries per hour set and that's being exceeded.
If you don't have SQL error logging turned on, turn it on and you'll be able to find out for sure what's going on so you can approach your host if necessary.
