Got a TN Laser, had it for about 8 years, no issues at all.
With out being able to see and feel the fabric its only guess work from me now.
I assume the tent has been looked after and dried out/aired after use before repacking when you get home from your trips, being damp would cause mildew i dont see how that would make it sticky.
The fabric is sticky, have you spilt any thing on the tent ? ever ? have you been popping bottles of champagne inside 🙂 could something have leaked onto it while in storage.
Take the inner out and hand wash everything would be my first step (i have seen the price of flys)
Have you used any fabric water proofers on it ? maybe that has reacted with the fabric.
If you have used the tent lots and lots maybe the fabric is starting to break down. Mine only gets used a few times a year so it will last longer than one used ever other weekend.
Give it a gentle hand wash, see what happens would be my choice, if that fails to cure it get in touch with Terra Nova.
Hope thats some help.