Delayed Overcurrent Protection
This is an electronics design forum. You could use a current sense resistor (shunt) and a current sense amplifier, and feed the output to a comparator. This will cover the current detection part of the circuit. Then it is just a matter of timing the excursion.

If you don't want to program a microcntroller, you could have the comparator output enable a digital timer (and reset the timer on falling edge). The timer can be set up to stop counting when it reaches a certain count (the timeout count).

If you don't mind programming a microcontroller, you could just feed the comparator output to an input on the microcontroller.

I do see a problem in your specification, however. Suppose the TX button is stuck. The timer starts counting, then at some point it cuts power to the radio. Now the current drops below 1A, and the timer resets, turning the radio back on. But the TX button is still stuck, so you immediately jump right back into the same problem.

Give it some thought.