How long can you tap the starter before it wont start at all?

When you tap on the starter, what you are actually tapping on is the starter solenoid; a device mounted on the starter (on most cars) that engages the starter gear to the engine gear while simultaneously connecting battery power to the starter. When the start solenoid gets to the point where you have to tap it, the remaining life is difficult to predict because it really depends on what's going on inside the solenoid (e.g. how many start cycles it has completed, exposure to elements etc.). However, the good news is you can normally go to an electric motor repair shop and buy a new solenoid for much cheaper than the whole starter, and in many cases, much easier to replace.