Lowering user's MySQL connections?

Hey all, tricky problem here!

My web page keeps going down for around an hour randomly.
My hosting has told me that this happens if a user exceeds 10 MySQL connections an hour.

How can I lower this?
I know its not a simple question but at what points do they even access it?

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Query limit is the maximum number of database actions performed in one hour by a specific user. Note that a user can have multiple concurrent MySQL connections, in which case the sum of all database actions for all connections cannot exceed the given limit.

The maximum number of concurrent MySQL connections per user is 10.

The maximum number of database queries per user is 75,000/hr.
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