If this has happened a lot, it may be happening because you are now expecting it to happen. Before you sleep, try to plan what you are going to do when you meet the desired person(s) Write out a scenario if it helps and think it over as you fall asleep, this will help with your expectation, you know what is going to happen when you see the person, therfore you won't be expecting it to end. Try to stick to whatever plans you made for the dream, after a while you should be able to spontaniously decide to do different things but this should help for the time being.
Have you tried rubbing your hands or spinning around when you notice the dream fading? if not these are proven methods for prolonging LDs
Hope this helps, I've never had this problem so my reply is meerly a stab in the dark.
Good Luck!