Same issue, changed my settings to see if made a difference it didn't. This is all but ruined PvP at the moment since you can't stay on your target at all. I can only imagine what its doing to PvE at the moment.
After further investigations it seems that the Click Unselects Target seemed to be causing the problem.
I have not encountered the problem anymore after having switched OFF : Click Unselects Target
Now wherever i click in my game HUD, the selected target seem to stay selected.
If the issue happens again, i will keep the thread updated.
I noticed this bug last night after a patch, I was only on long enough to do the Alhena mission. I was like WTF?! I turned off the click de-selects target and that worked for me as well. Also selecting a target will stay targeted until either you select a new target or hit the ESC key.
I had this going on too, moreso my targeting reticle would just vanish, nothing targeted but there was the occasional random switching of targets some those targets not even in range. It also made it nearly impossible at some points to target myself for a heal. I double checked my targeting options and their the same as usual, assist target off, target attacker off etc etc.
I'll try what some others have said, but I dont think I have click deselects turned on, moot point though, theres still a bug and it still should be looked at, I shouldn't need to change my setup to compensate for errors in the game.