I just figured it out. There is a conflict with a plugin called JP Custom CSS.
I used the process of elimination, turned off one plugin, checked Contact Form 7 – eventually found the one that it was conflicted with.
I can live without that plugin so I deleted it. It works now.
Same thing is happening to me.
It started happening after I deactivated the plugin and re-activated it. I was testing a plugin conflict issue so I had to deactivate all my plugins.
Unfortunately, I now have this problem. The contact form is still there but the plugin no longer works on the Admin Dashboard.
I clicked on the Donate button and donated hoping it would fix the issue but no such luck.
I don’t regret donating because it is a great plugin. I just want it to work again though.