Without context it is impossible to be 100% sure.
It probably means that they are to be separated for a while and he doesn't want to have sad feelings about her. When you miss someone, it means they are absent, but you keep thinking about them and wishing they were with you.
It could also mean he is throwing something at her and doesn't want to miss his target!
It could also mean that 'she' is about to perform in some way and he doesn't want to miss the performance. "Madonna is playing here next week. I don't want to miss her."