Site slow due to the amount of MySQL connections

[badger1010]

Our site sometimes suffers from slowing right down to the point where it is inaccessible.
Contacting support, they were able to see this and sent back this information:

I can confirm that your site was not accessible, I have taken a look and for some reason at this time your site had 94 active MySQL connections to the MySQL server. This is a long way above what an individual site should be causing, the result of this is that it was slowing the server down. Do you have any idea why your site would be making this many MySQL connections? Even a busy site being accessed by lots of users at once it would be very surprising if it went over 10 MySQL connections as these are not created at a rate of one per user. After your site had returned I checked the MySQL connections and there is only a single site on the server with more than one connection, and it only has 2, so you can see how excessive 94 connections are.

Can anyone help with this as it is outside my field of knowledge?

The site is ver 1.2.5.