If you have not downloaded the complete file it will automatically try to reconnect to peers to continue to download. It may not start back up if...
No peers can be found
Other downloads have been listed (by you) as a higher priority and there is a download limit set.
Another situation may be if you've deleted the torrent file. I'm actually not sure if the absence of the original torrent file will prevent the download from starting again or not. But keeping it around until you're done doesn't hurt.
Transmission will also automatically seed the file when the app starts. It may not restart if you have a max ratio set per file in the preferences -- if you've hit that ratio the file will not reseed.