greens should just dry out in the cage over time but shouldn't actually go bad. If the greens are fresh when you put them in, on the cool side, they should last for an hour or so before drying out too much. Misting the greens before serving will help them stay fresh longer.
Also, check your temps in the cool end, if they are too high, could be why the greens are wilting so fast. But it's not unusual for them to start wilting after an hour or so. If your dragons are not eating them at all, try putting their insects into the salad, making the dragons have to dig through to get the crickets and eating some greens at the same time. Cutting the greens really fine works best, as more stick to the crickets etc this way. If your dragons eat mostly salads, maybe serve less so they can eat the entire contents of the bowl before the salad has a chance to wilt.
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PHLdyPayne