Hello!
Hmmm. Let's see. Rats have one big eye, fur and and a large tail. Sometimes these things get damaged when you fight a rat, so sometimes there is no loot (the loot is generated randomly within certain parameters, this includes that none is generated). Believe me, if there isn't a new bug and the loot system works properly, rats do have a chance to give some loot. You should try a different rat as some NPCs don't generate loot at all.
But fighting is only one way. Maybe you want to try out the other ways as well.
With kind regards
Kaityra