I never in my 65 years of play, asked an opponent to resign.
But, I mostly played experts and masters and they knew when to resign and when not to resign.
I would just not play again a player who refuses to resign. There are too many players who might take it as an insult to ask for a resignation, even if you word it in a nice way.
Best to try and avoid players who do not know when to resign. One way to do this is to try and play against opponents much higher rated than you. The higher they are rated, the more likely they know when to resign.
If, it is a tourament, carefully read the rules of play. Some tournaments are set up to partially avoid this problem. Avoid tournaments with too liberal "vacations".
In correspondence play , not OTB right ?
Many excellent chess coaches tell their students not to resign until they are a certain rating (usually +1500 USCF).
Asking a person to resign is really offensive. As long as that person has something to learn from the game (such as the most efficient way to win), then he or she should NOT resign.
You're entitled to your opinion. I'm entitled to mine.