Trouble with TPMS sensors

[racing5k]

I have read through other TPMS topic threads and can't find my exact issue. I have had the solid light for a few months now and took it back to the tire shop and had it re-programmed a couple of times. Each time the sensors all respond through the horn correctly and the light resets. Unfortunately as I drive home the light comes back on. The only conclusion anyone can come up with is the the watch batteries inside the sensors are just to weak to send the proper strength signal to the control.
This puts me in a though spot because I would like to sell the car, and I don't want to sell it with this malfunction but on the other hand it's almost $250 with tax to fix!!!. The tire shop says I can't replace the battery in a perfectly good sensor, and this really makes me mad since it's a federal law! Let me know if you have any idea if I can replace these batteries.

Also, please tell me what you think this car should be worth?

This is a great little car!! I have owned it since new and drive it back and forth to work. I just bought another vehicle and don't have room for three cars in the garage. I will be posting more photos later tonight to show more details. For full disclosure- it has been bumped from behind while sitting at a traffic light and the rear bumper cover was replaced with a new one. No other damage was done. 4 Door with Hatchback 1.6 Liter Engine 84,000 Original Miles (going up daily as I drive to work) 5 Speed Manual Transmission Dual Front & Side Airbags Child Safety rear Door Locks Child Seat Anchors Cold A/C Good Tires Extra Clean Inside & Out Ready to go Vehicle Clean Title