Without seeing the tent for myself it is pretty challenging to diagnose the problem, but what it sounds like is an issue we see sometimes when the tent left pitched in the sun for extended periods of time or is stored somewhere (like a trunk of a car) that gets really hot. Basically the seam sealing tape heats up and can delaminate, lose its stickiness, and/or become brittle and flake off. I recommend using a light application of rubbing alcohol on a rag to clean the seams and help take off some of the pieces. When you are finished you can apply a seam sealer to the tent. Make sure you look for a polyurethane based sealant (not silicone) as that is more than likely the original sealant used. There is a lot more info located in this Expert Advice article for you to check out.
Best of luck and I hope this helped!