Re-searching & get more results tool can often help to get more sources for a particular file. But again, it depends on how many persons are sharing the same file. Also, some files are shared by ShareAza users who have a history of only allocating very low bandwidth toward gnutella network. Always exceptions.

So try the re-search option & also use the 'Get More Results' or 'Find More Sources' option by right-clicking the search tab a couple minutes after the search finishes. Repeat once or twice, then leave it for an hour or two before trying again. Don't do this too often for the same search criteria. Another thing to try is using a different search criteria which is similar to the one you used to find the file in the first place. That can take some imagination. For example, if it's music, try searching just the title of a song instead of the artist or vice-versa, perhaps not the same song you're after. This will help bring in more host results sharing similar files & help to extend your search across the network.

Torrents do have a lot of advantages over the gnutella network or similar networks. People are more likely to allow partial file sharing with torrents which speeds up the downloads for everyone & means much less work needed by the seeders (sharers) of the complete file.
I've had situations like uploading same video file to a few hosts at same time & was obvious at least a couple of them had partial file sharing disabled. So I was expected to upload the file individually to each one by myself. Those who disable partial file sharing make it somewhat harder & unfair on everyone else. If all 3 or 4 of the downloaders had partial file-sharing enabled, they would have downloaded the large file in 10-25% of the time.