I cannot think of any bike frame made in stainless so there may be a clue as to why that is not a good choice.
from my limited knowlwdge, stainless is more brittle than mild steel hence maybe the reason why - you would presumably be using a tubing that is some fancy steel alloy since these are engineered for bike frame puposes - i..e have thin walls and correct properties, unless you want your bike to weigh a ton. .... but for downhill that is not so important (but remeber you still need to get it somehow to the top of the hill)
As mentioned, the time consuming part will be the jig so that the frame rides true and you'll probalby need to practise not only your weldig but maybe make a couple of frames on cheaper steel tubes first.
Makes sure you post photos of your progress