I have intensely disliked 2 people my whole life, but my empathy never evaporated.
I chronically make excuses for people: They're just having a bad day, or past, or life in general. Maybe they're hungry or sick or suffering some other way.
For me, empathy and sympathy go hand in hand. I can't imagine one without the other, though I guess, I feel less sympathy for people who are habitually at the end of their rope. They can still tug at my heart-strings, as it were, even if I also feel annoyed and at a loss regarding how I could possibly help.
I give objects emotions though. I have a hard time throwing things out because 'how would I feel if I was discarded like that.' As a kid, I cried inconsolably, when my mom threw out toys or even clothes. 'You did that!' I told myself when I was all of about 5 years old and decided to paint a neighbors shed. 'You killed your shirt!'
Perhaps I'm just a lost cause rofl.
Actually, I take some of that back. My daughter is in the kitchen putting on a huge show because a bug fell or flew on her. She's laying on the drama extra thick with cries and shouts and squeals. I will temporarily lose empathy for highly emotional people. Especially if I feel they're not being genuine or are exaggerating an event. I don't handle loud noises or extreme emotional displays very well. It's not that I no longer feel anything for the person suffering, I just feel too much, so I react with anger and then shut down.