I'm a new Volt owner and can't really speak to other's problems with tires on the Volt but I have over 40 years of experience in auto repair/service, the last 17 years with a major tire company.
One of the most common reasons a tire needs to be replaced after a "flat" is that the tire was driven on after it lost most of it's air.
If a vehicle is equipped with a TPMS that merely warns of a low tire, often the tire is low enough that it overheats and starts to come apart.
I have always recommended that one should check tire pressure manually (with a good gauge) on a regular basis to prevent the "run flat" situation. Often a puncture is caused by a small object that causes air to leak very slowly. Catch the pressure loss early and the chances of a repair versus replacement will be more likely.
Again, I don't know your specific situation but generally, tires usually fail after a puncture because they were run in a flat, or mostly flat, condition. If your TPMS system actually shows tire pressures fine, but as a President once said "Trust but verify. Keep a good tire gauge on hand (The $10 one, not the $1.98 one) and check tire pressures regularly. I do it weekly when washing the vehicle.