Bricol
Basically we don't know but there are several theories, ranging from dry joints in the starter itself (caused by heat), to carbon dust falling into the solenoid from the motor brushes, to voltage drop in the long wiring from battery to the starter solenoid.
Try connecting a fly lead from the starter solenoid connection to the battery +ve. If this starts the car then there is a voltage drop in the OEM starter circuit.
Ensure your starter is in good condition.
So what can you do? Well do a search & see how some have solved (partially?) the problem. I have done the following:
1. Wrapped my Magneton starter to try & insulate it from the heat.
2. By-passed the starter relay in the MFU & shortened the wiring path. Incidentally the theory behind this is that the MFU starter relay gets carbon build up resulting in a voltage drop. This along with the long wiring exacerbates the problem, with the result that the solenoid cannot actuate the starter resulting in the click. The click is the solenoid travelling part way down its bore but not reaching the end. So now my starter button only initiates the new starter relay, which in turn switches 12v (from the battery) to the starter solenoid by the shortest path.
3. All starter & alternator wiring is enclosed in a heatproof sleeve & replaced every few years.
4. Starter relay is replaced every year.
Mick