Had the same problem with the tarp from a large Eureka family tent. Eureka said to launder it a few times in powdered (i.e. strong) detergent and most of the coating would come off, then recoat it with Aquaseal or similar.
I was able to get the coating off as they suggested. Now that the warm weather is almost upon us I plan to recoat it. Note these instructions are for polyurethane coatings, not for Silicon-coated fabrics. I don't think the latter become sticky with age.
Since I use old tents for car camping I usually bring a cheap blue tarp to throw on top of the tent if there are any leaks.