I think there's a few things that may be the issue.
Firstly: Are you asking directly? Not in a "we'd love to go out for a date night but no one will babysit, hint, hint," way? "We have a evening out on 9th October at 7pm, should be home by 11pm, baby will be in bed when you arrive. Can anyone babysit?"
I would ignore obvious hints, and not offer for vague "some point can you " but ask me a direct date and I'd check my diary and say "yes" or "no".
Secondly: You don't know if they're struggling. They may be struggling far more than you think and unable to give the head space to an evening out currently. You may share that-doesn't mean they do.
Thirdly: Are you expecting too much, or have a history of expecting too much?
3 people I know who have struggled to get any babysitters when mine were small I could have told them why people were not keen.
a) The long lists and expectation. First one, I nearly baby sat one time. I pulled out after their lists of demands grew ridiculous and included insisting (it was a daytime one) that I didn't pick my own (infant age) children up at school because it was their pfd's nap time. I don't think I had to read Shakespeare to their fish, but some of the demands were that sort of ilk.
b) Taking the micky. "Could you pick him up from school and just hold on to him for an hour so I can lock up at work" changed into the babysitter having a call at about 10:30pm clearly from a pub saying "I just went for a short drink with my work mates, we're going to a nightclub now-should be home by 4am, can you take him home and put him to bed and wait."
Unsurprisingly by the third time that had happened, most people had heard about it and the answer was "no".
c) You've done it once, now you're cornered for ever: This person would ask someone for a "desperately needed night out". They'd not been out for weeks, when would suit "babysitter" and they'd work it round them.
Then bam! They'd assume it was a regular arrangement-every Monday at 8pm, and would play the victim and huge misery if the person dared say they couldn't do every week.
Again, very quickly people were warned not to get involved.
If you're happy that none of those three apply to you, then try asking directly. "We're going out then. Can you baby sit?"
The best babysitters are those who feel that they can say no if they can't, but will if they can. I had an arrangement with a friend that if we didn't want/couldn't do it, then we said directly. That way we knew that there was no resentment about doing it.
I also found sometimes asking in a group more comfortable. That way no one feels putting on the spot.
But also when they're small, often the best people to ask were not other sleep deprived parents, but teens (for money) or grandparent age (who often loved doing it).