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Assuming the ambient temp has not radically changed (dropped), here's what you do:
Take the wheel/tire off the car, get a spray bottle of soapy water, spray it over the entire tire and valvestem.
Where you see bubbles, you found the leak.
II it's something on the tread of the tire, yes, it can probably be patched. If the stem, it can be fixed too. If it's a sidewall puncture, you may be looking at a new tire.
According to the following article by Hib Halverson, a Firestone spokesperson said the Firestone run-flats are not repairable after any run-flat incident (see toward the bottom of the article): Run Flat Facts
Look inside the valve stem cap as well. I once had an O-ring get dislodged and was actually depressing the schraeder core when I put the cap back on. This happened on a road trip, and I didn't discover the actual problem until the third or fourth stop to check my tire and air it back up.