Contacts deleting themselves every time I close the App

Shut off iCloud contacts, keep or dispose of existing contacts at the prompt, wait a couple of minutes for iCloud to realize it’s really off, reboot the Mac, re-enable iCloud contacts, wait a few for iCloud to realize sync is on and probably select merge, re-import the contacts data, and then see if the problem persists.

I’ve had iCloud get itself tangled on a few devices, and there’s unfortunately no reset button.

For the cases I’ve met, the combination of toggling iCloud around a restart of the problem iCloud client seem to have resolved the confusion.

Above assumes your network is entirely stable. iCloud really doesn’t like an unstable network connection, and gets very cranky.

Hello, Steve Burke.

Sorry that you're having this issue with your Mac.

If rebooting your Mac doesn’t fix things, see if the problem still happens in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode disables loading third-party drivers, forces the OS to clear certain caches and logs and does other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Does the problem persist while in Safe mode?

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.