They don't even have to be androids to pursue this thought. There could be a method to clone you, flesh and blood, with every last physical detail perfectly in place, then your thoughts all transferred over via some scientific method. So, there's an identical 'you' sitting there. You could clone it and copy the thoughts to the clone over and over for infinite time. Would you do it?
I would argue that the new clone, even with all your thoughts passed on to it, would still not be 'you'. It would have it's own perception of the world, and it's own self. So sure, I'd do it, but it still wouldn't be me. Call it spirit, call it soul, call it your own being, the id or whatever the hell you want, but 'you' won't be copied in a physical manner.