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Some shared hosting plans have very severe limitations on how many simultaneous database connections can be opened at any one time. Unfortunately, this is rarely ever mentioned when they are promoting their plans. They promote the plentiful drive space and bandwidth, which is very appealing if you have at least a moderate traffic site. However, increasing traffic means an increasing need for more available MySQL connections.
You may want to ask your hosting service about how many concurrent database connections they allow, and if they have an upgraded plan that allows more connections. Although, they my try to sell you on a semi-dedicated, dedicated, or virtual server option. Those are good options for many reasons, but they become more costly.
You may also consider moving to another shared hosting service that is more generous with their database connections. Hosting services do vary quite a bit regarding how my connections they will allow.
On the other hand (as others mentioned), using more of the caching features and upgrading to at least 2.0.14 my solve your problem (temporarily at least). Although, there still may come a point where your traffic becomes so heavy that you need to move to a dedicated or other option.
Dave
