In that scenario, I will right-click the 'Stalled' download file & choose 'Resume', hopefully it will attempt to reconnect to the host. Sometimes if you have too many downloads from same host, the host can only handle one or two of them, and the rest will perhaps wait for a while then go into Stalled.
If the search results had just come up & you did as I suggested, if the file does not show any effort at connecting properly then the host may have all their upload slots full.

I do find occasionally people remove some of their shares. So you will be very lucky to continue downloading those ones unless you can find another host with identical file.

I try to keep my shares static, if anything continually adding to it lol. Only exception is I sometimes change my share preferences, thus instead of sharing videos, pics & music, I might be sharing more music & videos. I don't do this too often though, rotating between the two sets of shares.