I am not a eunuch, just a wannabe, but I've had quite low testosterone my whole life. Not enough for doctors to insist I need hormone supplements, but low enough they've considered it.
That said, I've been single all my life, but whether it's an incapacity to love, I can't say; I think I do, but then again, I've never fallen in 'love'.
I've fallen in lust, though, many times, from the age of 9 or so. But it's never been a desire to fuck. Rather, it's been a desire to either cuddle (albeit very actively) and some oral desires, or, it's a situational desire; more about paraphilia or other kinks/fetishes.
I have loved my family members; siblings, parents, cousins, in the familial sense. I've loved my pets (although I've always been a bit blase about their deaths). I've loved my friends, in a fraternal way and more, in the sense I care deeply for them. But I've definitely never met any person about whom I could clearly say; "I wish this person would be around me, nearly all the time, for the rest of my life".
Every time I've tried to live with somebody (women, as a couple; men as room-mates and as a couple) it's taken a maximum of 6 months before I find myself hiding in the bathroom or shed multiple times a day just to have a moment to my fucking self.
This has been a problem only for other people who notice it or with whom I share it; as a rule, people seem to think 'pairing up' for life is as natural as breathing, and yet almost everyone I know outside of my own nuclear family has either divorced or had a series of intense live-in relationships that end rough.
For me, my life choice is ideal. I can't imagine spending my day raising kids, or having to talk to the same person about the same things all day every day ad inifinitum. Many have suggested I'll regret it when I'm old and alone, but I know old folks whos wives have died and they are having a fine life. And I can't imagine being comforted by being surrounded by 'loved ones' as I die in a hospital, like the TV says is the ultimate blessing; I don't want to SHARE that experience with anyone other than a paid caring nurse.
All that to say; I don't know if eunuchs fall in love. Hope that helps!

haha
