Does an IP address constantly change?

That all depends on what connection type you have. Can you tell us what you have?

Constantly no... occasionally most likely unless you pay more for a static IP connection.

Also depends on if you've got a router between you and the internet. If you do, that shouldn't change, but if your router is powercycling or something odd is happening with it, then your internal ip might change, your external one probably won't.

Can you be more specific as to what this is related to?