I have the very same problem in my site. I am going crazy. It was working, I update to 3.1.1 and (maybe for this or maybe not) doesn't work anymore.
I have been dealing a long day with it and I cant fix it. I change to default template, I disable/enable the cache (plugin and global), I delete the user and created again but nothings works, I logged in with "incognito" browser window, I removed all fields and try to save.
Isn't a way to figure out what is going wrong more than?
Error- Data integrity check failed, you are not allowed to save this item.
PONCHIK wich mistake did you fix, maybe this could enlight me