Hi Janeai,
We understand you're getting repeated sign in prompts for FaceTime. We're happy to help.
Open the FaceTime application, then select FaceTime up in the menu bar and choose Preferences. Once you've opened that page select Sign Out. Once you have fully signed out of your Apple ID account, go ahead and sign back in to it.
Once you've done that, test out FaceTime and see if you're still getting constant prompts to sign back in.
If you are still getting sign in prompts, go to System Preferences > Your name at the top, then sign out of your Apple ID. Once you've fully signed out, go ahead and sign back in to your account. After doing that, test again and see if you are still getting constant prompts to sign back in.
Use FaceTime on Mac
If your FaceTime app is still making you sign in frequently, we'd recommend contacting Apple for assistance: Get Support
We hope this helps. Cheers!