No beast so fierce but knows some touch of pity.

Nobody is entirely without an opening. The hardest person you deal with has something they are soft about, some person or memory or principle that gets past the defences, and it is almost never where you expect to find it. This is not naive optimism about people; plenty are genuinely difficult and some are dangerous.

With the person you have given up on, stop pressing on the place that has never worked. Find out what they are soft about and speak to that instead. And keep your own softness accessible, because a person with no visible opening gets treated as an obstacle rather than a human.