Aishes Chayil:
It is disingenuous to assume that you know the rationale of the one who is REFUSING to grant mechilah.
Are you SURE that the one who is refusing to grant mechilah wasn’t harmed financially because of the comments made by the person apologizing?
Are you SURE that the person didn’t suffer a breakup of other relationships as a result of the comments made by the offending party?
Are you SURE that the forgiveness is being asked in the proper way?
For the aggrieved party to hear ‘excuses’, ‘forgive and forget’, ‘it’s time to move on’, ‘it’s your problem for holding a grudge for such a long time’, etc. that infuriates them even more. Similarly, if the ‘apology’ only comes on Erev Yom Kippur, it’s a feel-good thing for the one asking the ‘apology’ and is frankly meaningless.
Another point…
Did the person say “NO, I’M NOT MOCHEL”, or did he hang up, slam the door, walk away, etc.? THESE AREN’T THE SAME. Saying that he’s not mochel means the onus is on the person to apologize in a meningful way. The other actions means the onus is on person to KEEP AWAY and leave the aggrieved person alone.