May be never. But there is a mechanism by which Earth may eventually be repopulated.
35 random people scattered all around the globe is apparently too few for repopulation. However, the reappearance mechanism described in this question is very resilient and can provide a very long term supply of new residents. How long?
If a person who reappears can secure shelter and food supply, he or she can live potentially a very long time. Let's assume post-reappearance life expectancy of "survivors" at 20 years. On the other hand, after a relatively short period of time, all resources left by civilization (houses, tools, weapons) will be gone, and survivors would be mostly on their own. this means that only a fraction or resurrected people will be survivors, most will die relatively quickly. Assume that a person has 1 in 10 chance of becoming a survivor, and non-survivors, for statistical purpose, will die instantly. This gives us average life expectancy of 2 years for all reappearing people. Earth population currently is 7.7 billion, and there are 35 people living simultaneously, which gives us 110 million years before humanity would die out. This figure assumes that there will be no any significant repopulation during this time. Also we've come to a conclusion that at any given time most of Earth population will be survivors rather than "succumbers".
One stipulated rule states that "Disappeared reappear where they were at Disappearance, if a Reappeared dies. If the space is occupied, they appear in the nearest fitting location relative to the Earth", and here the definition of "occupied" and "fitting location" is unclear. For example, if cities like New York and Mumbai will get flooded, reappeared people may appear in water and any survivors among them will be unlikely. I assume here that "fitting location" should be suitable for human habitation, thus the above figure of 110 million years should stand unchanged.
In addition to that, there will be a very slight force which will draw survivors together. As mentioned in another question's answer, HAM radio will make survivors aware of each other and they may form groups. Let's assume that withing first 100 years after the disappearance event, a survivor has 50% chance to use radio and establish contact with other. Learning how to use the radio is not very difficult, if books and actual units are still around. However, after 100 years chance of finding working radios and components will go down significantly.
Anyways, there is near certainty that survivors will form a communication network which should live for at least 100 years after the event. This will allow survivors to learn about how disapperance/reapperance work.
- Most population disappeared, but there are still few people around;
- There are reapperarances. Reappearances occur in the place of initial disappearance;
- Reappearances are linked to death of living people;
Some survivors could be just fine with living solitarily, but most would be expected to try to join together. This desire to congregate is that "slight force" which can eventually lead to repopulation of the world.
However, it would be difficult for the survivors to travel long distances. In the first years after the event travel for 100s of kilometers would still be feasible. People in densely populated regions would be expected to meet and form small communities. Let's assume that 50% of HAM radio activists will be able to travel. This leaves us with 25% of the population (8-9 people) actually living non-solitary lives. Of course, some traveling survivors may die in the process, but this causes only a temporary delay - there will be new survivors willing to travel.
In addition, departing survivors will try to make things easier for those who reappear after them. For example, if someone had lived alone in New York, but then learned that there is a single girl in Florida, he might leave some big signs saying where to find his caches of supplies and which radio frequency to turn to. This, at least, should push the percentage of HAM radio users above 50%.
However, after the initial period, roads and cars will deteriorate and long distance travel will become problematic. I assume that after about 10 years after the even, only 5% of survivors would be able to make a successful trip to join with the others. Still, that gives us 3-4 non-solitary people at any given time.
Now, let's get to the reproductive math. Disregarding any new births, we will be having 4-5 potential couples in the first 20 years, and 1-2 couples after that. Assuming that survivors will tend to be healthy and fertile, I will assume that 50% of those couples will have children. Let's further assume that the couples would try to have many children. Now we are unfortunately in the territory of wild guesses. Let's assume that fertile woman will have 6 children, and 4 of them will survive into adulthood. This would mean that the world population will be over 35 people within the first 20 years and reapperances will stop (at least temporarily).
Even after we have some thriving families, next phase may be even more problematic for repopulation. If everything goes well, in 20 years we have a happy family with 4 young and 2 older adults, but what's next? To continue procreating, available options are either more travel, or inbreeding. Both options are problematic, either in short or long term, but in both cases natural persistence would prevail. If families would choose to travel, some would not make it, but small percentage would be successful. If families choose to inbred, many would die out within a few generations, but small percentage would win the "genetic lottery" and produce healthy offspring. There are real life examples of species restored from a brink of extinction with only a few specimens.
Thus, in all likelihood, people will keep procreating. However, before human communities will hit a certain "critical mass", this would be a slow process with much "back and forth". Once there will be a few thousand people in the world, the process will become unstoppable, and it may take less than 1000 years to repopulate, but it is very difficult to say when people would get out of the initial "population bottleneck phase". This phase may be as short as 100 years, or many thousand years long. Good news is that we have 110 million years to keep on trying.