Some options: Get the milk from the bad quarter cultured to find out what pathogen you're dealing with. If it's antibiotic-resistant, it may come down to the cow eventually clearing the infection on her own ... or not.
If that's not feasible, you could just go ahead and try treating with a better antibiotic. I'd suggest Spectramast (you'll have to get it through a vet). Treat at every milking, and keeping treating until the infection clears or until you decide to give up on that quarter, whichever comes sooner.
Four treatments with Today really aren't enough to get the job done in most cases, even if it IS a pathogen that generally responds well to antibiotics! On the farm where I work, frankly we don't even bother using Today (or Tomorrow) any more ... it just isn't effective on the bugs we're dealing with.
I'd use Spectramast's dry-cow treatment at dry-off, too. I have seen chronic cows treated with it freshen in with no further problems ... sometimes ... but very often, chronic cases are just that ... chronic.
If the infection doesn't respond to any of the above, you could just quit milking that teat. Eventually it will dry up. Sometimes, as Gone-a-Milking indicated, an abscess will develop, and those are nasty and unsightly, but not necessarily fatal.