It sounds like an overheat failure
This picture shows the miniature 32 channel transmitters as supplied (before overheating) and a New Zealand coin to indicate size.
I have used, seen and repaired some video transmitters with very poor thermal design. Overheat failures are quite common. Many underestimate the need for cooling. The VTX produces heat even when the model is not moving; unlike the ESC.
It is probably a reverse polarity protection diode that has failed; if it is a series. If the board has not been badly burnt, it may be repairable.
Measuring the current draw before extended use is a good idea as it gives an indication that all is well. An antenna fault or connection problem can greatly increase VTX current draw and heating.
Video transmitters are very inefficient; transmitted power is a fraction of the power in. Therefore a lot of heat is dissipated in the transmitter. Voltage regulators on transmitters are almost all switching types now, to reduce the heating problems; but it’s only a partial solution.
I sometimes include a switch to turn the VTX off while the model is on the bench or waiting for GPS lock etc. It reduces internal heating when there is no flight induced air-flow; and it saves the battery. Also handy if you want to swap or adjust the VTX antenna without powering down the model.
I recently bought two 200mW and two 600mW miniature video transmitters from China (just arrived – pictured above) for my mini-fpv-wing project. VTX power supply and cooling are major design considerations. It will have RTL, but it’s always a good idea to include a reliable video transmitter.
