Keeping within the official Doctor Who canon, is it possible that the Doctor could transfer regeneration energy to his past self an unlimited number of times? Is there any aspect of the Who universe that would indicate that this is not possible?
I'm not certain that transferring regenerations between himself at different points in his timeline would work as supported by Who canon. Of course, if a writer felt such a solution was the answer to a problem, everything would be Timey-Wimey and such a feat would be accomplished regardless, but I can't point to any extant material that supports such a scheme.
That said, it is possible to gain more regenerations. The Doctor received a new cycle of regenerations from the Time Lords in The Time of the Doctor after all! Similarly, the High Council of Gallifrey offered a new cycle of regenerations to the Master in The Five Doctors, and the Master claimed in The Sound of the Drums that the Time Lords resurrected him to fight in the Time War, granting him a new cycle of regenerations in the process.
The exact system for granting a new cycle remains unexplained.
You have two glasses. A[ ] B[ ]
You fill one up from the tap. A[=] B[ ]
You wait 5 minutes then travel back in time. pA[=] pB[ ] fA[=] fB[ ]
You pour your full cup into your past self's empty cup. pA[=] pB[=] fA[ ] fB[=]
Where did the extra water come from? Answer: there is no new water, it's the same old water. The water started off in cup A in the past; it then got carried over to cup A in the future. That water was then poured from cup A in the future to cup B in the past. The water is then in cup B where it remains in the future.
At one point during all this, both cups are full; but for both cups to be full a cup in the future must be poured into a cup in the past.
Change the cups for timelords and the water for regeneration energy and you see that it's impossible to create infinite regeneration energy, the energy always has to go somewhere. The transfer is set in stone, any deviation would cause a paradox or some similar time problem.
If you prefer to think in terms of timelines, the energy/water's timeline is a linear piece of thread. All time travel does is fold the thread in on itself; the thread is still the same thread.
Here's a diagram, with time passing from left to right:
No, he has a limit. This was addressed in The Deadly Assassin, The Doctor Who movie, and confirmed in The Time of the Doctor. If you rewatch some of the episodes, you'll see that the War Doctor does count as a regeneration (and is actually the true 9th incarnation), then he regenerated into the 9th Doctor (10th incarnation), then he changed into the 10th Doctor (11th incarnation), then he regenerated and almost changed in The Stolen Earth/Journey's End (making him the 12th incarnation, possibly, but with the same face), and then he changed into the 11th Doctor (13th incarnation). In the special, the Doctor mentions that every single regeneration counts, including his Warrior one, and the fact that his 10th/11th incarnation regenerated twice, makes it so that the 11th Doctor was always going to be the face he dies as (hence The Fall of The Eleventh). The Time Lords ended up giving him a new regeneration cycle, proving that he couldn't just give himself regenerations, because if he could, the 10th Doctor might have avoided changing for god knows how long. Even with the new cycle, we're not sure how many regenerations he has now, but he clearly has a limit.
My short answer is "Yes! Doctor Who is potentially immortal."
Feel free to prove this theory wrong after considering the following:
The Doctor has met and even touched himself without any life threatening problems.
See Has The Doctor ever met himself?
What is true in the Doctor's past is true in his future. In The Day of the Doctor, the War Doctor begins running some calculations on his sonic screwdriver which are completed on the eleventh Doctor's sonic screwdriver. This was apparently a rewrite of history in which the eleventh Doctor's screwdriver had not been running these calculations until that event.
Time Lords can transfer regeneration energy to one another. Melody Pond uses an entire regeneration worth of energy, sacrificing her final regeneration, to save the Doctor's life in Let's Kill Hitler. In The Angels Take Manhattan, the Doctor heals River Song's broken wrist with some portion of regeneration energy. In The Time of the Doctor, Time Lords transfer regeneration energy to the Doctor, allowing him to regenerate into his twelfth incarnation.
The Doctor's Dupe Regeneration Hack
To avoid the paradox of him committing suicide in this process, let's say the Doctor has at least one regeneration left. He goes back in time just ten minutes in his own time line and transfers that regeneration energy to his past self. His past self now has two regenerations available. In theory, the future Doctor will now have two regenerations available as well.
If the future Doctor instantly receives a new regeneration upon transferring it to his past self in the same way that the future sonic screwdriver had been running calculations from the past, he could repeat this process until reaching his full capacity for regenerating energy. Then he could return to his time line, ten minutes in the future, and go about his business.