This is normal, to add a bit more info to the above comments, this is how anvil damage works. With each use, an anvil has a 12% chance to become damaged – degrading one stage at a time, first becoming chipped, then damaged, then eventually destroyed.
And to add onto what @iSneaky said, this vanilla mechanic works regardless of if it’s in a protected town or not. Also fun fact, I destroyed a trade sign that I didn’t own at Colebex a long time ago because it was placed on an anvil, and I broke the anvil.