In the first post you said the tape was coming away, then later said it wasn't peeling away.
Anyway, I had old Berghaus jacket, bought second hand before I knew how water proof jackets were made exactly, and the seam tape had come away from the seams in some areas. The tape itself was drier and less flexible than fresh tape, and the tapes adhesive had dried out, cracked and become flaky, powdery and crumbly.
The tape on your tent has basically started to decay, and the only way I see of fixing it is to remove the tape, clean the fabric of any residual adhesive, and re tape or use seam sealant to re water proof the seams.
I'm always weary of buying waterproof stuff second hand now, especially if you can't see taped and sealed areas.