Mars is also unable to maintain an oxygen atmosphere, isn't it? At least at Earth-type temperatures.
It should be, but estimates range from a few thousand years to a billion or more. More research would be needed.
And the atmosphere would probably be mostly nitrogen (or some other buffer gas such as argon, but the relative rarity of such gasses makes them less attractive).
The bigger problem would be hydrosphere loss due to water being disassociated by UV rays, as happened on both early Mars and Venus.
EDIT:
Where would we get all that gas (of any type)? Siphon it off of Earth - and reduce it's atmosphere in the process?
No. Aside from the ecological concerns, Earth has a large gravity well which makes gas transport impractical. Nitrogen and water would probably be sourced from outer solar system objects like comets.
Why would we create a breathable atmosphere, or even normal atmospheric pressure when taking off our space suits outside of a habitat would result in fatal UV and solar radiation burns (due to a lack of both ozone layer, and magnetic field). And how could we even create that much pressure when the gravity is so weak?
Cosmic radiation (and charged particles) don't cause fatal burns on contact (AFAIK), at least not the type you are describing. Add to that the fact that even a thin atmosphere provides shielding.
For UV, you could either attempt to synthesise an ozone layer or wear sunblock or clothing.
As for holding onto an atmosphere- I point you towards Titan. Even a small body can hold onto an atmosphere, the question is for how long.
Teraforming doesn't really make sense. Plus it also corrupts the solar system, which is a bit of a crime for all humanity and all future generations.
Compare a living, livable world to a dry, vacuous dustbowl and tell me how that is corrupting.
Better to just build giant habitats. That way "The Red Planet" stays red, we get to stay there without a space suit and actually relax, safe from all the hostilities of space, and don't have to spend a billion years or destroy other planets in the process of trying to do it.
You will not have no worries if inside a giant habitat- cosmic rays, pressure differentials and even the odd meteor impact will be an issue.
Add to that the fact that you will have to wear a spacesuit to leave the habitat (for repairs or otherwise)
And terraforming Mars won't take billions of year- the most optimistic estimates put it at even a few hundred years.