Unfortunately, due to Mars' lower gravity and lack of a magnetically active core, not only can it not hold a substantial atmosphere to begin with, any such atmosphere would inevitably be blown away by solar winds.
So there's that. Maybe we can put a big dome around the whole thing like Planet Druidia.
The timeline for that process is millennia, so if we come up with a continual process for replenishment that works on shorter timeframes, it's maintainable.
> MAVEN measurements indicate that the solar wind strips away gas at a rate of about 100 grams (equivalent to roughly 1/4 pound) every second. "Like the theft of a few coins from a cash register every day, the loss becomes significant over time," said Bruce Jakosky, MAVEN principal investigator at the University of Colorado, Boulder. "We've seen that the atmospheric erosion increases significantly during solar storms, so we think the loss rate was much higher billions of years ago when the sun was young and more active.”
The entire solar system is an inherently unstable construct. Luckily for us the instability is on a scale of billions of years. Terraforming mars would be similar. It would be a herculean effort that would take several lifetimes to complete, but the result could be stable on the scale of millions of years without further input. With a bit of maintenance it could well be stable for the life of the solar system.
So there's that. Maybe we can put a big dome around the whole thing like Planet Druidia.