From what I can tell, nothing ever gains audience over time; everything loses audience; and the best you can hope for is that the hemmorhaging won't hit cancellation levels before the story has had a decent chance to play out.
Well, word of mouth and advertising can always increase audience from an initial small viewerbase. The classic example is Cheers, which finished dead last in the ratings in its first year and then went on to be a monster hit. It's the would-be success story the fan of every single cancelled series claims his show would have been with a little time and lovin'.