I am on my second playthrough and experienced no problems the first time around and didn't up until a short time ago: I have Alistair, Morrigan and Leliana in my party. Alistair will continue to fight but Morrigan and Leliana will not fight...even in the bigger battles where there are enough enemies that the ones Alistair and I cannot engage quickly enough will attack both of them and they still will not fight back. Here's what I have:
1) They have free movement. Hold is not active and Alistair still acts appropriately.
2) I have tactics properly set which had served me fine the first 1.5 times through the game. Even set them to aggressive and they still won't attack even when being assaulted by enemies.
3) I went to the party camp after the end of the section where the problem popped up to see if that would end the problem when getting back into the game but the problem persists. I have not yet gone back to the camp to change parties to see if other members will fight or if this will continue.
Honestly, Alistair and I have been fine without the other two helping in battles but I'm about to head to the Landsmeet again and I would like to see if there is a way that this might be fixed.
I do not know if it's related but another 'problem' I ran into was my first time in Denerim in my second playthrough... went to the Pearl and talked the White Falcons into leaving. The Pearls Before Swine quest states that it is ready to be completed by talking with the head Guard. I spoke with him in the cutscene following us leaving the Pearl but when I walk up to him in the Market he tells me the original lines of dialogue about be going to the Pearl and beat the White Falcons up but not kill them.
I mention this only because I experienced neither problems on my first playthrough and then both seemed to happen about the same time this time around.
I cleared the system cache and re-downloaded the game update but problems persist. I've finished the rest of the game and had to start the Landsmeet. Guard Captain still wants me to go to the Pearl and deal with the Falcons but they're all gone. And upon approaching Arl Howe's estate Alistair and I fought off the soldiers alone.
I went with the same lineup upon leaving Arl Eamon's estate to see if this problem had been fixed which is appears to not have been. Morrigan and Leliana stand in the same spot, most of the time with their backs to the action, but as soon as Alistair and I kill all of the enemies they catch up and follow along. Basically they're acting like the NPC following us to Howe's estate.
After completing this part and being given the opportunity I will try to swap out at least one of Morrigan/Leliana for another character and see if they'll fight. I just find it odd that it's not the whole party doing it and that Alistair continues to fight.
I did not completely reset my 360 as I do not currently have a method of backing up what I'd lose for all of my past games played.