Is there a way to avoid losing my progress when Uplay is down?
Solution 1:
Nope, sorry. I've run into this myself and you can't get the saved games from the Ubisoft servers, you will have to start anew with the campaign in offline mode to not depend on their servers which right now may be lacking stability.
They are very well known for this DRM, see Assassins Creed 2, which unfortunately didn't offer an offline mode like HOMM 6.