We bought a used Kenwood TK-5710 off of E-bay 2 years ago, us being the 2nd owner. We were just having the exact same issue. The palm mic is used so much, unless we squeeze the button hard, it keys up at first, and then it drops out by itself.
So we just got a brand new palm mic from our local Kenwood dealer last week & threw out the old one. Unsure how old it was, no date code on it.