MySQL problem: User has already more than 'max_user_connections' active connections

[Mirrorball]

I created a test installation of Drupal, a CMS, on my server yesterday. Many hours later, I started getting MySQL errors from vBulletin (too many connections) in my inbox. Even though no one was accessing Drupal, the errors wouldn't stop until I deleted the MySQL user and created another. I changed all my scripts to use the new username and everything was working again. Then, a few hours later, the same problem happens and I change users again. At this point I deleted my test Drupal installation and no more errors occured.
What could be causing this? Drupal is not set up to use persistent connections. I had installed a couple of modules I created myself, including a vbulletin integration module. I suppose I could have made a mistake and a module could have an infinite loop, but it didn't look like it. And wouldn't the script time out eventually and release the connection link? My site wasn't very busy either, the first errors occured at 8am, not a high traffic time. And why did I have to create a new MySQL user to make the site work again? Does it make any sense? I'm very confused, I have no clue about what could be causing the problems. My site is at a shared server and last month was far busier than this one and I didn't have any problems.

vBulletin and Drupal were using the same MySQL user the first time it happened. Then I changed the user for Drupal, but the vBulletin module was still using the same user as vBulletin.