Hey Polarbear -
The cause of the problem is most likely caused by the lack of DC current getting to the radio as other have said (could be SWR related, but it would not be the most likely issue). If you haven't already done so, check to be sure the radio is on "low" power. As you know, those rigs put out 25 watts or more on low power and as much as 60 watts on high power, a real current sucker.
Sometimes the lack of DC current issue isn't quite as obvious as some may consider. Here are some steps you can take to determine where the problem is (could be one or more involved):
1. Connect the power leads, at least temporarily, directly to the battery terminals. Be sure there is a fuse between the radio and the battery (I know the TM271A has a fuse in line but just not making any assumptions). Check the radio on low, then high power to see if it works.
2. If the radio doesn't work after the first test, remove the inline fuse, clean the fuse holder and insert a new fuse. Try the radio again to see if it works.
3. If the 1st and 2nd test don't work, check and inspect the DC power connector on the radio. It doesn't take much for the wires to come loose inside of the connector something that may not be detected by just looking at it. Try wiggling the wire as it goes into the connector as you transmit to determine if a loose wire might be the issue. Better yet, if you have a VOM, use it to determine if there is continuity from one end of each wire to the female end of the power connector.
I'd say that if none of these three steps identify the problem then it's something other than a DC current issue. Could be really bad SWR shutting down the rig, or something else internal to the radio that's bad.
As an aside, I have a couple of TM271A rigs, so please feel free to PM me if I can be of any help.