Magento checkout problem (failed orders) - probably MySQL or PHP memory problem

We have a Magento website running on a 1and1 VPS (4GB RAM), with around 3,000 products.

Recently we have been having many orders failing in the checkout, after clicking "submit order". Sometimes it keeps loading indefinitely and sometimes it empties the shopping cart and redirects back to the home page.

The server should be powerful enough to run this website efficiently, so I believe the problem to be a MySQL or PHP script or memory leak. I have attached the PHPinfo file and a screenshot of the resource logs from Virtuozzo.

It also may be worth noting that we have installed an additional separate Magento installation on this server, but this is not yet public and so currently receives no visitors (except for development and testing).

The job is to fix the issue or faulty script. Once complete we will need to wait a few days to ensure that the failed payments have stopped (as they occur at seemingly random times).

Please ask me any questions that you have.