Seems pretty normal what you’re describing. It sounds like you’re almost getting the music memorized but not all the way through. I would try to visualize it all the way through. Figure out where it is you’re stopping, is it always around the same place? If so, work from there on bit by bit, this way you’ll eventually get to the end by memory. Memorizing music is like memorizing a poem or lyrics… it can be done bit by bit, in this case more like bar by bar.
