You can do it daily, but try not to go to failure too often or you may develop pain in your elbows or forearm flexors.
When I first joined the Marines, I was a big strong guy, but was absolutely horrendous at pull ups. I think I was only cranking out maybe 11 dead hang by the end of bootcamp. When I got to my first duty station, I decided to fix this by doing a sub max set every time I passed a pull up bar. For those that have never been on a Marine base, they're everywhere, so it's impossible to avoid them.
I'd end up doing several sets a day (I never kept count) and would stop 1 or 2 rep shy of failure. My pull ups improved very quickly. Now, they refer to this method as "greasing the groove", but I swear I came up with that shit first.