I set the delay to 2. I tried waiting 2 days, but the trigger still didn't work.
The child nodes I'm talking about are "dead end" nodes (there are two of them, neither works). The other nodes, the ones that do work, either trigger a new dialogue, or an event (though this latter trigger isn't working for me). My guess is that the game is not able to finish the dialogue when it reaches a dead end, so it just doesn't activate the child node that has no triggers.
Edit: I found the culprit. Both dead-end nodes that weren't working featured the 'Emotion > Sad' effect. I removed that effect from both nodes, and now they work correctly. Thank you for your help. Still no fix for the event triggering effect, though.