That stored procedure runs every time the application starts up to do some DB cleanup that helps keep the site in PA-DSS compliance. If the DB server is running slowly or the DB is overly large, that can sometimes take a long time to complete.
The best way to keep this from happening is to run Monthly Maintenance regularly through the admin console. Some sites get busy enough that it needs to be done more frequently than once/month.
You can also have your developer look into archiving off old data to keep the DB size down. Many sites find that there's just no need to have really old order, customer, address, etc records in their production environment. You can pick a date that makes sense based on your site and move that data out of the live DB, into some kind of backup somewhere. There are lots of different ways of handling that and it's not something we can assist with, but your developer ought to be able to help out.