Why does silver sulfate not precipitate in this double displacement reaction?
Since the lab is past due now, I'll give what I think is the answer.

$\ce{Ag2SO4}$ is somewhat soluble in water. It is most likely that you simply didn't get enough to cause precipitation. 

The other possibility, which I don't think applies here, is that you have a supersaturated solution. There are some precipitates for which crystals are just stubborn to nucleate.