Not really a car guy

I have a 2006 impreza which of course is AWD. My rear passenger tire had a slow leak in it, I put a can of fix-a-flat in there and that sealed it for a good month or so, I was at my parents house a few days ago and when I went outside to leave, I saw that the tire was flat again, my Dad and I looked for a nail or anything that may have punctured the tire, but didn't see anything. The other tires are still in great shape, they easily have another year or two on them. If I take my car to a shop and they tell me that the one tire is shot, am I really going to have to buy four new ones or is that just the dealer trying to get more money from me? I've just heard that when you replace one tire with AWD you have to replace all of them, is this true?

i take it you have the alloy wheels. there has always been problems with slow leaks on alloy wheels. any corrosion build up on the rim can make a slow leak around the bead of the tire. before you go replacing 4 tires have the leaking tire dismounted and cleaned up bothe the rim and tire to insure a good seal. and for the record dont ever use fix a flat unless its an emergency! now your other question about having the same tires on all 4 wheels. yes always keep the same size tire on all 4 corners to prevent drivetrain damage. if you have a brand new tire on an a used one with tread worn off they are not the same size. hope that helps