This could be an issue with the concurrent connections limit on mysql. If you have too many users the checkout may be timing out as a result of the stalled connections building up and taking too long to process.

 

You may want to consider a vps where you have control over something like that by optimizing mysql.

 

Its a lot of work to move a wordpress site to another server temporarily but it can be done relatively easy if you know what you are doing.

Mike L. | WebPro