Drupal not closing database connections correctly?

My site, culturecat.net, was yanked twice by my hosting service (Site5), the first time on May 23 and the second time yesterday (May 28). The first time, I was using 4.7.3. After that, I did the following to reduce server resource usage:

# Deleted all seven of my subdomains
# Upgraded to Drupal 5.1
# Reconfigured my robots.txt file so that ONLY Google can crawl my site
# Disabled the monthly archives and tagadelic modules

Okay, so after all that, they yanked the site again, after I upgraded and did all the other stuff. They said that I should check to see if persistent database connections were enabled in Drupal, and if I read correctly, they were not. Their email:

Hello,

The problem is that your site is opening too many SQL connections and not closing them:

6918 | culturec_db | localhost | culturec_culturecat | Sleep | 44 | | |
| 6925 | culturec_db | localhost | culturec_culturecat | Sleep | 43 | | |
| 6948 | culturec_db | localhost | culturec_culturecat | Sleep | 29 | | |
| 6949 | culturec_db | localhost | culturec_culturecat | Sleep | 29 | | |
| 6962 | culturec_db | localhost | culturec_culturecat | Sleep | 19 | | |
| 6964 | culturec_db | localhost | culturec_culturecat | Sleep | 19 | | |
| 6966 | culturec_db | localhost | culturec_culturecat | Sleep | 19 | | |
| 6967 | culturec_db | localhost | culturec_culturecat | Sleep | 19 | | |
| 6995 | culturec_db | localhost | culturec_culturecat | Sleep | 13 | | |
| 6998 | culturec_db | localhost | culturec_culturecat | Sleep | 12 | | |
| 7008 | culturec_db | localhost | culturec_culturecat | Sleep | 11 | | |
| 7020 | culturec_db | localhost | culturec_culturecat | Sleep | 6 | | |
| 7023 | culturec_db | localhost | culturec_culturecat | Sleep | 6 | |

Please make sure you are not using persistent connections.

I told them Drupal didn't seem to be using persistent connections, and here's what they said:

Persistent connections via PHP scripts is disabled server side as this is only really useful for connections from remote sources. I suspect you may be encountering a bug within the application which is preventing it from closing database sessions correctly. You may need to file a bug report or support request with the Drupal developers.

Also, interestingly enough, my site works fine in a way. I set up a redirect, so that now if you try to go to culturecat.net, it takes you to my wordpress.com blog. But you can go to other URLs in my site, and they load without any problem. For example:

http://culturecat.net/cv

http://culturecat.net/taxonomy/term/14

I asked Site5 about this, and they said:

When you implement a re-direct within your control panel this alters the .htaccess and drupal relies heavily on .htaccess modifications so I supect that any changes you may have made are conflicting with those already in place. Your error log data within your control panel should have more information for you.

Please, is there anything you can tell me? You should also know that I've looked at the logs for the time they took the site down, and there aren't any spikes in traffic or unusual activity.

Oh, and by the way, I know that some people have had trouble having Site5 host their Drupal sites. I'm not having a very productive or satisfactory experience with them right now, but it's relevant that they've hosted my site now since 2005 without a denial of service. It's also pertinent, perhaps, that the plan I pay for includes (theoretically!) unlimited usage.