Determining the cause of a strange "the other side can't hear me" issue
This doesn't really answer the question, so just for the record if anybody else has the same issue:

I don't know about other phones, but small Sony Ericssons have an interesting feature. They have small buttons in the corners of the screen. One of them is muting the microphone. And... as the user rises the phone to his ear, the screen that was turned off for the call turns on because the phone is moving, and the ear hits the mute button with an 50% chance. The other side swears and hangs the phone, so when I finally see the screen turning on again, the button and the mute sign isn't there yet.