There was a weird problem I faced with Magento on Bluehost server. The site keeps throwing error saying there are too many connections with MySql database with a single user. On contacting the hosting provider they said they allow maximum of 15 concurrent connections for a single DB user. while 15 is not a good number by any means, it's not very bad for a newly started website either. It's less probable that 15 users are attempting connection to the DB at a moment. But the error log consistently showed me this error and it was far too often.
I tried to look at the phpinof.php file to see if there is anything abnormal related to the MySql settings. Yes, there was a surprise for me. The persistent connection was set to ON in that file. Apparently this had to be THE problem. When I checked in the php.ini file there was no such setting so I assumed that it comes from the default php.ini settings. So I set it to off in my PHP.ini file. Since then, I have not faced this problem.
Although this problem is solved for now, I'm sure it is going to come back at some point of time as 15 concurrent connection is not an adequate number. But it gives me a breath for the moment!