On May 1, 1996, approximately 2145 mountain daylight time, a Piper PA-28R-201T, N175WW, owned and operated by a private owner, was substantially damaged during landing at Peyton, Colorado. There were no injuries to the private pilot and two passengers. Visual meteorological conditions prevailed at the time, and no flight plan was filed for the personal flight conducted under Title 14 CFR Part 91. The flight originated at Pueblo, Colorado, at approximately 2125 mountain daylight time. The pilot said after making a normal landing, the airplane began wobbling. It then veered slowly to the right and the right wing struck a taxiway sign. The pilot said he had checked the tire pressures two weeks before the accident and found them correctly inflated to 30 psi. Also, the tires appeared normal during his preflight inspection prior to the accident flight. Postflight inspection, however, revealed the right tire was flat. When the hub cap was removed, the valve stem fell out. It had separated from the tire tube. The pilot said it appeared the valve stem had not completely bonded to the tube.