Database issues – max connections

I’m sure this comes up hourly. My host allows 10 connections to the MySQL server at the same time. They say thats normal for any large site. My site gets 2,000 unique visitors a day, which is a lot for me but I’m sure not a lot for a large WP site. I’m getting the database error page a lot now. On and off all day today. They say its because some script isn’t closing database connections so I should disable persistent connections in the script. I have no idea how to do that. I’ve checked my PHP settings and it has mysql.allow_persistent set to off.

Is 10 mysql connections normal, or a really small amount? I don’t really have any major plugins running. I’m trying to decide whether I need to go through the hassle of swapping hosts if mine is indeed not doing their job.