On my iPhone, the mic could be re-enabled during a call by pinching the iPhone tightly at about the same point as the noise cancelling mic (next to the headphone jack). This would cause the mic to kick back in for a few seconds after you stopped pinching the device.
Tellingly, directly under the metal shield in that exact location are three press fit connectors for various IC's. I folded a small piece of paper and laid it across the backs of those three connectors. I then re-attached the shield and replaced the back cover. Mic problems seem to be gone for now (crossing fingers). I'm thinking that in some cases, the connector for the noise cancelling mic works a bit loose (or perhaps the sponge used to keep pressure on the connectors compresses somewhat). Time will tell, but right now, it seems to be working again.