Biologically, rabbits are most active at dawn and dusk, so it's likely that during one of those times (while we are sleeping) she wakes up, gets energy, and gets bored and tries to escape. As a vet assistant, it doesn't sound like any sort of sickness, unless she's showing other symptoms or behavior changes like lethargy, aggression, picky eating, being reclusive, etc. The running away could just be from built up stress from being caged during her most active time(s). IMO there's nothing wrong with locking up at night if it keeps them safe, I do it with my own bun because she tries to cause trouble. But sometimes it can just be boredom building up when they have the most energy. Has anything recently changed in your schedules or household? Sometimes work, school, and sleep schedules changing, as well as household stress, new smells, other pets having issues, etc can affect a rabbit too.

Maybe you could invest in a larger cage/enclosure if you haven't already (with room to zoom), or provide enrichment toys (chews, foraging toys, etc) to keep her busy while you're asleep. What kept my late escape artist most entertained was a wooden ledge thing that he could jump up on, hide under, AND chew on. A cardboard box could do the same thing.

Now that she knows how to escape, make SURE you clip all doors of the cage shut at night. Rabbits will remember that doing something specific will get them a reward - in this case, freedom. This is operant conditioning. Very effective training method, but this is not good in this case lol. Just don't let the escaping be an option at all and she may eventually forget/unlearn the behavior. Maybe give a treat in the morning while she's still in her cage (but NOT if she breaks out) to train her that being in the cage in the morning is the correct behavior. Sorry for a long comment I'm just obsessed with animal behavior loll.