Civic - Honda :: 2008 - New Tires But Tire Light Blinking?

Sunday I had a new set of tires put on my Civic. They told me that one of the four Tire Pressure Monitoring System sensors was bad and that they'd have to order me a new one. I drove home that day with the TPMS light on, which was expected.

This morning I went back to the shop and they replaced the bad sensor. However, after resetting, and doing whatever else it is they did with the handheld computer thing a half-dozen times, the Low Tire Pressure Indicator light is not only on, but blinking. (The TPMS light is off). They drove it around, they checked it with their computer thing again, they plugged in the handheld thing to reset it, went around and did something at each of the tire stems multiple times, but no matter what they did, the light wouldn't (and won't) stop blinking.

"If it doesn't stop on its own, you might have to bring it to a Honda Dealer."

Seriously?

I used to have an old Aurora that would turn on the engine light every time a reading went slightly out of whack, and after so many ignition key turns (on and off) the light would turn off on its own. Is that the case here? Or is this light going to blink forever until I go to the Honda Dealer?