Imessage on Mac keeps sign out

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later. 

Isolating an issue by using another user account 

If the problem is still there, try booting into the Safe Mode using your normal account.  Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer or by using the developer’s uninstall instructions. For each disable/delete, you will need to restart if you don't do them all at once. 

Safe Mode - About.    

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

https://etrecheck.com

It may be your Apple ID. Someone I know had this happen and I was able to sign in using my Apple ID. After a call to Apple Support and then being elevated to a tier 2 support person, it turned out it was a problem with their Apple ID. It took the software engineers 3-4 days to fix the problem.

When calling Apple, make sure you tell them it is an Apple ID problem so you don't get charged.

There is a contact link.

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.  (The link doesn’t always load)

Get Support    Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport

its not about vpn or anti virus, i used another account then i can use imessage normally. But my account still kicking me out when i signed in