The taxi driver is Zeus, or Hades, or a collective apparition of the Greek godsAs is pointed out within the film itself, the name of the ship, Aeolis, is a reference to the figure of Greek mythology. His father, Sisyphus, was condemned - by Zeus, by Hades, or by all the Greek gods, depending on how you interpret the old myths - to forever roll a boulder up a hill, only to see it roll down again, a fate clearly intended to mirror Jess's imprisonment in the time loop. Zeus, or Hades, or whichever god/gods inflicted this punishment upon Sisyphus, clearly felt that Jess deserved the same punishment for abusing her son; so they created the time loop, then manifested themselves in the human world in the form of the taxi driver in order to lure Jess into the loop's beginning. Poor Jess is, in other words, doomed to repeat this experience for eternity.
Heather doesn't existHeather is listed on the main page under What Happened to the Mouse? because after she falls off she's never seen or mentioned again. If you go with the theory that Jess is in purgatory and this is her punishment then it's possible Heather only exists in purgatory (for whatever reason) and vanishes after she's no longer relevant.
Jess can break the cycleFollowing the Cab-Driver-is-Zeus/Hades/Death/Whatever theory. Jess' labor is Sisyphean, but the powers that be may be merciful. All she has to do is return to the cab instead of restarting another cycle, thereby honestly fulfilling her agreement with the driver. But to do that, she'd have to finally accept her son's death. As long as she can't let go, she's doomed to keep reliving the day.
Heather survivedFollowing the theory that the group died in the capsize and are now in hell/purgatory, Heather going missing may indicate that Heather survived the accident and therefore did not die and is not suffering the loop. Her occurrence in future loops from Jess' perspective may indicate she may be in a coma periodically entering the loop, or is simply a projection of Jess' hell/purgatory.