If you are in plat you will only get matched in gold/plat games or diamond/plat games. If there aren't enough people in those ranks queueing you will simply never find a game. Most of the time queues for ranks below diamond die out during the season and you have to wait for the next season to find ranked games again.

Platinum is an especially bad rank to be in after the first few weeks of the season because gold players tend to get put with unranked/bronze/silver matches and diamond tends to get put with crystal/omega/ultima matches.