... Yes, that is your problem.
When you are downloading, you actively seek people out to trade data with. Once you've completed, your client shifts its attention to other torrents. You might be able to reduce the effects of dropped connectivity by forwarding your ports properly, but don't expect major changes.
This is a minor issue compared to the big picture. If you know how the BitTorrent protocol works and how leecher and seeder counts matter, you'd see why your lack of torrents is your problem.