I second D's post but with a little extra info. While it is dangerous to offer adult mice because they can harm your frog the frog's skin while sensitive is tougher than most people think. If you ever have to give them an injection you'll discover this when you notice that the needle is having difficulty penetrating the skin. An adult mouse can and will hurt even adult frog since they can bite pretty hard and scratch. The scratching is really only bad around the eyes.

Mouse fur can and will impact the frog if your not careful. From now on when offering mice use pinky mice or fuzzies. An adult mouse will take about a week to digest.

They do occasionally sleep with their eyes closed. More than likely this is caused by you having the Light up on full blast. If you have a UTH on the side its should help maintain temps. 76° at night is fine, but keep it at 80° during the day. Having the light on full will also suck humidity out so keep an eye on it.