I'm given to believe that as far as Honda cars in the US are concerned it is a fact that there are a finite number of stop starts before the starter warning light come on. However, the warning light will flash until the starter is replaced. It will not render the starter inoperative, and the starter will operate normally until it mechanically fails as any other starter would.
Honda maintain that the starter motor on the stop start variants have a very robust starter. Presumably the same logic would prevail in the UK with exactly the same parts and engine management system.
The number of finite stop starts is presumably not known to anyone but Honda themselves but with their engines having such a good record for reliability and commonly exceeding 250K miles the number of vehicles affected must be very small. (Although evidence of this nature is frequently leaked as in the case of Volkswagen and their emission lies which cost them a great deal of money.) If it were a generally known fault affecting many thousands of vehicles Honda owners would be up in arms and there would be recalls on the grounds of safety. Why Honda should have gone down this route in the quest for a few more mpg is difficult to understand given the potential problems likely to arise.
Having said all that it is very pleasing at a prolonged enforced stop when the engine switches off to imagine you are doing your bit for the environment and your pocket.,
Mr Hick's remedy is in your hands.