This can be fixed by moving the materials to a different inventory slot and then doing the evolution. Not sure why it is broken as I haven't been able to get it to the broken state on my own profile.

For me the Evolve button is there and makes the sound when you click on it but nothing happens..

Did you try moving the evolution material to a different slot in the inventory?

moving the materials did nothing but one day after a game all my materials vanished when i visited the town, confused i went back to private tavern and they all returned since then i can evolve normally

Moving material fixed the issue for me.

It's also happening with me. I have the materials and the gold, but cannot evolve a pet.

I’m currently having the same issue with a pet. I went to evolve it and it clicks but does nothing. I went to switch the pets between characters my huntress and squire and both pets vanished. Now I dont have the pet I was trying to evolve nor do I have the pet that was already evolved. 

*A few few hours after posting & playing*

I checked my scavenger. Some how my pets went from my characters straight to the scavenger.  I don’t know how it happened but if anyone has an issue like mine check the scavenger in town he might have your pets. 

Have this issue ongoing. I read this thread and now check which material I need. Just switching that mat to any other possition in the inventory lets me evolve. I've evolved three pets recently and all of them needed this trick.

2 of my pets at level hatchling can't evolve when i already have gold, items, pover and affection (10/10)  to do that.

There is evolve button available but with no use. After click there was only sound effect.

what happened to me today is.... yesterday i evolved my pet and it had its ability and today i log on it was 10/10 on all thing lost the ability and now its not evolved.

This will be fixed as of our next release.

Nothing worked until I let a bunch of eggs rot the evolve worked again! :--)