Je me permets de vous rappeler que la date limite est le 19 novembre.
This carries the assertive strength of
If I may/could/might (in order of assertiveness) remind you that …
(I assume the difference in French will be the tone of voice.)
These are classic understatements: the greater the understatement, the greater its force.
The "may" is assertive but mild - the implication is that permission is sought, whereas the real implication is that permission is irrelevant.
The "could" is assertive - It implies that the reminding is something that, possibly, may not be necessary, whereas the real implication is that the speaker is sure that the listener has forgotten or ignored the criteria and that the reminding is essential.
Might is very assertive - the implication is that the speaker is unsure that he has the rank or right to point out a fault, whereas the real implication is that the speaker is furious, he knows he is superior to the listener, and that the listener is an idiot.
Je me permets de vous demander si vous pourriez m'aider sur la rédaction de ce contrat.
I hope you don’t mind my asking … This is polite and deferential.