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I've completed both Jack and Miranda's loyalty quests. They then have this scripted argument, and without the proper paragon/renegade you have to basically pick a side and the other one gets mad at you and loses her loyalty.
Can you talk to either of them at a later time and get that person back to being loyal or are you stuck after this scripted event?
Like raznagul already pointed out, you can regain their loyalty later.
But you can also resolve the conflict without picking sides if you have enough paragon points. (Maybe renegade points work, too, but I didn't have that at the time of my playthrough.)
It also says so on the Mass Effect wikia:
Shepard can resolve the conflict without picking a side, in which case, both Jack and Miranda agree to put off their fight until after the mission with the Collectors is over.
You can later regain their loyalty.
Source: http://masseffect.wikia.com/wiki/Miranda#Loyalty http://masseffect.wikia.com/wiki/Jack#Loyalty
Upgrade your soldier ability to Shock Trooper ASAP. This gives you +100% paragon/renegade. Then charm the person who is angry with you. I sided with Miranda then upgraded to Shock Trooper and I was able to charm Jack to win back loyalty.
