Transitions require what are called handles to work properly.
You cannot start with the actual last frame of the clip at the beginning of the transition or the first frame at the start of the next clip. There have to be frames there for the transition to use, that are outside the edit.
So say you're using a 15 frame transition.
Both clips must have at least 15 frames available as 'handles' for the transition.
In other words, the end of clip 1 on the sequence MUST be at least 15 frames before the end clip 1. And the beginning of clip 2 on the sequence MUST be at least 15 frames into clip 2.