I am not a server admin as most of you know so please pardon my ignorance!

I have a client who has a server at their location which allows viewing of a secure camera.

Their ISP is Cox.

They are supposed to have a static IP which is the location a user gains access to upon successful login.

The static IP resets a few times a year for some unknown reason.

The latest info I received included:
CAMERA SYSTEM IS SET ON IP ADDRESS: xx.xxx.xxx.xxx
Assigned STATIC IP: xx.xxx.xxx.xxx
Gateway: xx.xxx.xxx.xxx
Netmask: xxx.xxx.xxx.xxx
Primary Name server: xx.xxx.xx.xx
Secondary Name server: xx.xxx.xx.xx

So is there a way to have this accessed via a subdomain or domain name that never changes?
If so, how would I make sure the reset doesn't affect the ability to view the camera?

Any help/suggestions/feedback would be greatly appreciated!