1.) check to make sure you companion is set to 'follow' and not 'wait here' before fast traveling. There might be conditions that will set your companion to 'wait here' without your knowing it. Remember that there are certain areas (like the casinos) where you character cannot follow. When you enter such a place, your companions is automatically set to "wait here."
2.) when you are moving through broken terrain, and especially when you are doing jumps and otherwise forcing a difficult crossing, always look behind you and see if your companion can follow. I've noticed that companions can duplicate some feats of movement, but not others. When a companion cannot get to where you are the way you got there, it will try an alternate route, which (given the broken terrain) may take it on a long and winding route away from you. This is how some companions 'just vanish' and then end up being killed somewhere by themselves. So if you see you are going to cross some rough terrain, do a save first in case you companions ends up running all over the place.
3.) This one I'm not sure about but it worth looking into. Watch out for area that are within areas. I.e., the Strip is inside Freeside, which is inside the Mojave. If you are inside of something that's inside of something, you may have to go completely to the original outside again for your fast travel to take your companion with you. At each stage of getting outside, check that you companion is still set to 'follow.'