I, too, have had this issue. I drag a cross dissolve to end of last clip and it doesn't "stick," just disappears. Wanted to confirm this before posting and I think what the original poster and I are doing is dragging the dissolve transition to the end of the clipas though to place it at end of clip and 'nothingness.' I just tried doing same thing but placing the transition ON the last clip NEAR the clip's end and it worked!
Im sure this is exactly what I was doing lol. When I get home I will give this a try and see how it works for me. Thanks everyone for the suggestions and help!