I am getting Mysql Server Gone Away error in Database Connection

This could happen due to 2 possibilities

1. Poorly optimized php scripts which takes a lot of time to execute and hence mysql quits processing
2. If there are too many mysql connections opened from your website which makes mysql to quit

Also make sure that you are closing mysql connection after you open and use a connection. This could also be a reason.

If you feel that your usage is genuine and your website is well optimized and such a usage is required, then please upgrade that particular account alone  to Higher Package