I love the "I'm no expert...BUT" disclaimer before you give the wrong advice to someone who really needs anything but. It does not really matter what a month in the primary "SOUNDS" like to you, because anyone that I know who makes awesome beer (including me, not blowing my own horn but my beer is often as good as many craft beer offerings) leave their beers on primaries for more than a month at least. Often, I will brew up 5-6 beers in a 2 week span and just leave them... bottling them slowly as I need the beer, over a 3-4 month period.
To OP, looks like you are getting some good advice from some other posters though, and I would suspect that this is most likely a water issue. Personally, I had serious problems with Rubbery/Bandaid before and it happened to be from my starters - I was shaking my starters during fermentation and then pitching the entire, oxidized starter liquid on my batch. As soon as I started decanting the liquid the problem went away. Are you doing this?