100 years in the future, Mars has been colonised. New settlers and resources arrive from Earth every 26 months (when the planetary orbit lines up best) by first taking the space elevator to Earth orbit and then using a large one-way ship to get to Mars. The ship is designed to be one-way, landing on Mars and then stripped to be reused around the Martian colonies, a Mars space elevator is in the works, which, once completed, would allow true two-way travel between the Earth and Mars or at least that was the plan before the blackout happened.
One day all communication with anything outside Mars stopped (Earth, the next colony ship that was in route to Mars & even the crew working on the Mars space elevator in Mars orbit), an event that among the Martian settlers came to be known as the blackout, no one knows what happened, but for the purpose of this question, it's safe to assume that every human being outside Mars is dead and every man-made machine outside Mars stopped working.
The technology of the Mars colonies is near future (100 years) earth level. Things such as food, water and air have been fully self-sufficient even before the blackout with Mars-based greeneries, fish farms, algae farms, and vat-grown farms providing food, fuel (biofuel), bioplastics & a certain level of medicine (basically any form of medicine that can be grown), it also provides some building materials (wood & bamboo) while some other resources (stone, sand (for making glass) metal, water, earth elements) are mined on Mars, the only things that were dependent on supply from Earth were things that are so advanced that they couldn't yet be produced on Mars, like the more advanced parts of computers & cellphones, advanced medicines, advanced robotics, etc.
The colonies' electricity comes from multiple sources, solar panels (imported from Earth) provide some power, but mostly it is either nuclear power or from burning local biofuel.
Mars is not terraformed, and the colonists live in a mixture of domed cities, caves, underground areas & above-ground buildings made from local stone & metal.
Travel between areas of the same colonies never requires stepping outside an unpressurised area (underground subways being the most common form of transport in larger colonies and walking in tunnels in the smaller ones), travel between colonies is usually done with pressurised above-ground vehicles and trains but some colonies which are close enough to each other also have underground transport from one another.
While most Martian colonists are Earth-born, there is a small (but growing) number who are Martian born. Giving birth on Mars has proven possible with about the same level of difficulty it is on Earth; it's entirely possible to give birth on Mars without any medical assistance, but most still prefer to see a doctor (much the same as on Earth).
Mars is, in fact, an array of colonies connected to each other, each providing some resources to other colonies, but no single colony is the sole provider of any resource. There is some friendly competition among the different colonies in much the same way that some city residents in the same country like to talk about other cities. Still, when the blackout strikes, they pull together to survive.
Martian colonists put a lot of emphasis on being as self-reliant as possible, even before the blackout. 3d printing and machine shops are common occupation on Mars as well as other productive professions (there aren't a lot of advertisers on Mars, assume all colonist has useful skills or are young and still in school).
Assume the colonies are of the minimal size needed to survive long term; if your answer requires a minimum of 10,000 people to survive, then that's the colony's size; if it's a million, then a million it is.
Can the colony, as described above, survive long-term? For this question surviving means the most basic of needs being met, if they have water, air, food, a place to put their head for the night & the ability to give offspring who will get the same, that's enough, even if any sort of luxury they used to have is gone in the process.
As time passes, what resources they had from Earth will break down, and if they are required for survival, they will need to be replaced with a locally made substitute. Is there any piece of equipment or resource that couldn't possibly be made by the colonists that is required for survival on Mars?
If the answer is no, please provide the exact reason why the colony can't survive, don't just say, "They couldn't possibly reproduce anything needed without Earth's help", but rather say something like "X requires the element Y which doesn't exist on Mars and can't be synthetically manufactured dooming everyone".