Yes, as indicated above. Mids who leave voluntarily, and in good standing, can re-apply. Of course, the hill they have to climb is doubly high, and they have to explain how they have changed to everyone along the way, demonstrate they have not wasted a year, continue to meet all standards, etc.
The mission departures and reapplications have been going on for a long, long time, and as long as the mid departs in good standing, maintains physical readiness and good conduct, he/she is usually folded into the class two years junior to the original one.
Female midshipmen are required to leave if pregnant. They can apply to return if they are not the guardian (the exact term escapes me), i.e., the child becomes the responsibility of someone else, and they are not paying parental support or assuming parental responsibilities. Same deal for male midshipmen who father a child. If they assume a parental role or pay child support, they must leave. These situations require lots of family support.
I knew a mid who left during plebe summer, saying "not for me." She attended a civilian college, realized she had made the wrong decision, re-applied, climbing said hill above, and got back in the next plebe class. She was injured in the first few weeks, and was released for medical reasons. She went back to college and intense physical therapy, re-applied, and several classes behind her original class, went on to successfully gain her commission at USNA.