Hi. I have the same problem...
I bought some tetras on sunday from a new lfs. I left them to settle and on monday morning I checked them to find one had white stuff on and around th base of its dorsal fin... (didn't spot anything in the tank, and they all looked healthy). when I came from work, one had died (had white stuff around its mouth), yesterday (tues) another had died (no signs on this one) and this morning the one with the white fin had died. I added King British Fin Rot and Fungus treatment last night, and none of the other tetras or my gourami have any patches on them.
I'm going to treat again tonight (it says every 24 hours until symptoms disappear) and probably again tomorrow, with half a dose if there is still no sign. I'm just hoping thats the last of the losses (my water test says everything is fine, and I introduced them over the space of 3 hours, slowly adding water from my tank to their bag so I don't think it was anything I did - before anyone says anything, I don't have a quarantine tank, but I will after this experience, we all learn trough mistakes).
If you're sure it's fin rot, get some treatment that treats both that and fungal problems (to cover your bases), and take out the carbon from your filter so it doesn't remove the medication.
I hope you get it sorted. it's devastating when something like this happens