From an engineers point of view, I know that the leading edge anti-ice system is controlled by temperature and the anti-ice valve will open/close at a certain temp (the fig 110 springs to mind but am not 100% sure)
However I cannot quite recall, but am fairly certain that the inlet anti-ice valve also has a temp sensor in the duct, before the valve if memory is correct, and this if overheated will also close the valve. I think it would take a considerable amount of time to cause any real fatigue problems as a result of excessive use provided that the system works correctly - i.e temp sensors work and that the valve hasn't been locked out.
I would however also add to what has been mentioned, that Boeing will have assessed all eventualities and would only publish advice/recomendations that are prudent in operating the aircraft.
Just as a slight aside but not to far off this thread - as pilots does anyone know if there have ever been cases of 737's with CFM56 engines that have flamed out on descent at idle power, in heavy precipitation, even though the spinner is now rounded as opposed to conical?
I had heard/read that it may of been the cause of the loss of an aircraft recently - was it in the Far East, aircraft finished up in a river, not many casualties?