MyBB Community Forums

That's because too many people are connecting to MySQL, your host will need to raise it, or just tell people not to visit your forum. If too many people are trying to connect to your host than what they allow there's really very little you can do. Do you have a shoutbox or anything??

No shoutbox.

I'll have to check into the number of allowed connections. What do you guys recommend for a small but busy MyBb forum?

I recommend finding a better host.