Unless your personal safety is threatened on the street or by an intruder in your home, let someone go from a submission as soon as they tap!
Trusting that your opponent will do the same for you is crucial to a good environment on the mats.
There is no shame in tapping. If you know your partner has you, why grit it out for any reason other than ego?
On the other side of the coin, if you think you could escape a submission attempt, don't tap, try. I've known people to tap as soon as my arm shot under their neck... I hadn't even applied any pressure, they just didn't want to be in that position.
The hard part about accepting being submitted or submitting your partner is, that you haven't lost or won anything and should move on from the moment to go again. That's why I believe outside of competition there is no 'winning' because it's all just practice.
Get tapped or land a submission 1000 times and tell me you haven't learned anything...