Namaste Mukesh
I tried to personalize customer Card it took me max 1 minute to publish .
Verify below things which can cause this issue
1) Page which you are trying to personalize is custom or Standard page ?
2) Any developer doing the customization at the same instance
3) Can you personalize some other standard page and confirm
4) Can you check permissions given to you in your user-card
5) Can you verify some other sandbox environment and verify
6) Can you relogin with other user and try to personalize the same
7) Ensure no update activity is happening in the environment .
Personalize page should work .
If you feel this helped , please verify the answer . Or you can reply to this post .
Regards
Pallavi Phade
