as a general rule you cant fast travel when enemys are near by
NOW if you where in combat and you did a runner your enemy will still be hunting you down even if he is out of your radars reach (and it dose not show a red dot)
this usualy happens with city guard when you comit a crime, you wont be able to fast travel untill you cross the borders into a new Hold
the same with NPC's like the Cultrist of Boethiah he will track you for a very long time
some animals do this like trolls, mudcrabs, bears ext
so although you think you can fast travle you cant because something/someone is still chasing you
you can get arond this by going into the sneak position for a few seconds .... after that your enemy will lose you just like in normal sneaking
so you can fast travel after that
the other way is to backtrack and kill whoever is chasing you .... but that might take you a long way back untill there red dot apears again on your radar
NOTE with the three thugs .... you can fast travel befor they say "we are hear to teach you a lesson" but once combat starts you cant ...they will track you indefintly until they kill you or you kill them