Does Major Cage Still Have the Reset Ability?

After thinking over the movie more, I am providing a second answer that is not necessarily contrary to my other answer.

The strongest evidence that Cage does retain the ability to loop is his final loop itself (at end of movie, when he wakes up in the helicopter near Big Ben). Clearly his looping ability has been restored, and there is nothing in the movie to suggest that final loop was a one-time-only deal.

The scene where the omega's blood interacts with Cage plays out nearly identically to the scene where the alpha's blood interacts with Cage, suggesting the same sequence of events is occurring. I believe this is meant to show that Cage got the looping ability from the omega in the very same way he previously got it from the alpha. Same transmission method and same ability suggests same rules of retaining ability.

Cage did not lose the original looping ability from the alpha until he bled out -- so why would he have lost the second looping ability from the omega without having bled out?

I think the events and symbolism of the movie suggest that, at the end of the film, Cage does not have the time-looping ability, or at least does not need it. The loops have served their purpose: he has matured into a responsible, loving adult.

Notice how the movie comments on the human maturity process:

At beginning of movie, Cage is immature and selfish. In a position of privilege during a time of crisis, he playfully flirts with the pretty young woman who greets him at the helicopter pad. Then he tries to avoid combat by blackmailing the general.

The time loops offer Cage a chance to mature. He makes a mistake but then starts over, avoids the mistake, instead makes a new one, and continues learning in this fashion. Over and over and over. Like any person making their way through young adulthood. He works hard, and along the way, he finally really gets to know other people, and their struggles.

At the point when the loops stop, Cage has matured. He has recognized the value of other people and is willing to sacrifice himself for them. He is self-assured because he has conquered his demons. He has fallen in love.

By the end of the movie, Cage has dispensed of the pesky "alpha" force that had him losing the same impossible battle every day (a young man coming to terms with the alpha-male urges of young adulthood) and moved on to conquer the more important "omega" force that was the true cause of the suffering (a mature man having figured out how to live life in harmony). At the same time, this maturity also means he no longer has the youthful ability to bounce back unharmed from mistakes. A wiser man, he appreciates his life much more, now that he has realized it is precious.

If the Omega had not died, I believe he would still have the reset ability. The Omega IS dead, however, and the Omega was the entity resetting time when the Alpha/Cage died. So while he does still have the reset ability in his blood, there is no Omega to perform the reset.