Getting Logged Out After Signing Into iMessage on Laptop

Hello Cate216,

Thank you for using Apple Support Communities. Based on your post, you can't stay signed in to iMessage on your MacBook Pro. We'll do our best to assist.

You've done some good troubleshooting up to this point. If they haven't solved this, then we'd recommend the following:

1. Check System Status for any reported outages: System Status
2. Sign in to the Manage your Apple ID website and verify your account details: Manage and use your Apple ID
3. Quit the Messages app on your Mac. Then relaunch it while holding down the Shift key, to remove the app's saved state. Once it opens completely, you may release the Shift key.
4. If you're using a VPN or security software, we'd recommend to disable them and restart the device, as these may be blocking the connection.
5. Create a new Administrator user on the Mac and see if you can sign in there: Set up users, guests, and groups on Mac
6. Test safe mode and try signing in: How to use safe mode on your Mac
7. Check for hardware issues: Use Apple Diagnostics to test your Mac
8. Remove login items to resolve startup problems on your Mac

If the issue persists after these steps, then it would be best to connect with Apple directly: Get Support

Wishing you well, take care.