The alternating action of depriving Testosterone and then exposing Testosterone as an idea to extend the time for which hormone therapy works has been around for a while, and there is something call bipolar hormone therapy which does exactly this. In practice, this is done by staying on hormone therapy all the time, but delivering Testosterone for the alternate periods (because hormone therapy takes too long to switch off if you just withdraw it).
In practice, it hasn't shown to be effective, but I think it's only been tried near end of life, because it's probably considered somewhat risky and hence too unethical to try from the outset.
The nearest equivalent which is in use it intermittent hormone therapy, where those with slowly rising PSA are able to take holidays off hormone therapy, and only restart when PSA rises to a predefined level (per patient). In patients where this is viable, they generally spend longer off hormone therapy than on it, and it doesn't shorten life (although I don't know there's any evidence it extends it either, but it can give more quality of life).