Answer: As many as it takes till you can't patch it the last time.
I have one 26" MTB tube that has fifteen patches on it. Some of them might be two small round patches on a pinch flat, but it holds air perfectly well.
I'll replace it when I can't get a puncture to patch properly.
On the other hand I've had road tubes that won't take a patch for some reason - the butynol rubber just "rejects" the vulcanising fluid and after some minutes of test at pressures below 5 PSI it just lets go. Those get the valve cut out for bottle rockets, and are put on the "emergency tie downs" hook.
Of course I ride with a spare tube for each wheel size on the bike, and I carry sticker-patches as a last resort or to help other people. If its a long ride I'll sling a second or even third tube in. So even though a patched tube goes back into the rotation, its not the only thing I'm depending on.
My normal patches are "cure-c-cure" and weigh 9.3 grams for all 15 or 0.62g each. For comparison,
- 15 small budget orange-edged patches weighed 9.7 g or 0.65g each
- 8 medium budget patches were 7.7g or 0.96g each
- 4 other medium orange-edge patches were 3.1g or 0.78g each
- 1 large budget patch was 1.9g
Assume the weight of cured vulcanising fluid roughly equals the weight of the backing foil:
A 26" / 559 tyre with a rolling circumference of around 1.75 metres needs 87 patches of 20mm diameter to completely surround the outer edge.
87 patches at 0.65 grams is 56.5 grams. Which is not insubstantial but represents 1/11th of a full drink bottle or one large gel.
Those patches would cost you around $20, two tubes of gloop another $20 for a total of $40. Compare that to 87 new budget tubes at $5/each is $435 total.
Upshot "patch till you can't patch no-more" unless you're competing in a race where every gram counts.