So far, it appears Mars One will be one-way mission to Mars, to establish a colony with no options to return to Earth, astronauts staying on Mars to the end of their lives.
But does that mean the mission ends with death of the last astronaut, or is it planned to be expanded indefinitely, with continued shipments, colony expansion and new arrivals?
Mars One's Mission Roadmap on their website states that the first crews living quarters arrive, 26 months later the first crew arrives, a few weeks later the second crew living quarters arrive, 26 months later the second crew arrive, and on and on as additional living quarters and crews continue to arrive. Also eventually martian colonists will start having children in the colony.
Supplies will be needed, and in particular spare parts, as the base grows. In fact until Mars based in-situ manufacturing is able to cover most of the spare parts, the base is unlikely to be able to grow very much, if at all, in the beginning.
TLDR: No, once Mars is inhabited, it should remain inhabited forever.
First, the current answer is that the mission has already ended, since the Mars One organization has failed to produce a feasible plan to raise funds for a believable process to get there.
Second, no, Mars One had a plan which included sending four additional astronauts arriving every 26 months. Presumably there would also have been a significant number of babies born there.
While the Mars One bankruptcy puts all plans on hold, any successor who wants to raise funds from the public will doubtless keep the idea of a permanent Mars settlement a high priority.
The plan, as Mars One envisioned it
According to their roadmap[a]:
Settlement expands with departure of Crew Two The second crew will depart from Earth and the cargo modules for the third crew will be launched.
When the astronauts land on Mars, they will be welcomed by the first crew. Their living quarters will already be prepared. The hardware for the third crew will land a few weeks later and will be added to the settlement. This process will continue as additional crews and cargo modules land every 26 months.
That is not explicit about the babies, but the whole concept is built around a permanent settlement with a future and decreasing dependence on Earth.
[a]See Brooks Nelson's answer for more about the status of the project in 2015 and 2017.
The future?
It seems very unlikely that Mars One will survive as an organization, but anyone able to market plans for a Mars mission to the public while satisfying scientific realism could work with their ideas. I doubt if the one-way trip would ever be considered again, but if funding depends on public interest, the promoters would have to convince them of the intent to settle permanently.
