Error 503 indicates that your website has exceeded it's process limits. The process limit denotes how many tasks your website can do at once - sending/receiving email, displaying the website, doing shopping cart calculations, etc, all count towards the process limit.
There are two possible causes for this. The first is that the site's web traffic has grown beyond the capacity of the plan you are using and you might need to look into upgrading to a plan with a larger limit. Think of this as good news - it means more people are coming to visit!
The second possible cause is that certain parts of your website code are looping. When writing website code, it's important that the design is implemented with a view to economy of processes. If something has changed in your site, it's possible that some elements of the code are reacting to each other and triggering process operations not intended by the designer.
If you encounter Error 503 on your website, please contact us and we can do some tests to pinpoint the cause. This may involve manually stopping all processes to remove any loops present and will allow us to come to a conclusion about whether the cause is a simple matter of more users accessing the site than your plan can support (in which case we will discuss upgrading your plan) or if the issue is coding related, in which case we will refer you to your web developer to examine the code.