Typically, if a player is banned after a single game, it is due to their being something excessive in the logs. From the Instant Feedback System FAQs page:
WHY DID I SKIP RESTRICTIONS?
We have a zero-tolerance policy for extreme negative behavior as well as extremely offensive language and remarks made in game towards other players. Since it is a severe disregard for the Summoner’s Code this sort of behavior can result in skipping to a Two week or Permanent suspension. Suspensions of this degree based on negative behavior will not likely be reduced or removed.
If you would like us to look over your logs and give you an idea of what in them might have escalated you up to a ban, feel free to post them here. They should have been posted as part of your Reform Card when you try to log into your account, and you should receive them in an email as well. Often times, the use of hate speech (any racial or homophobic slurs) or any sorts of comments regarding self harm (kys) will bump a player to a first time 14-day or even permanent suspension, as Riot has a zero tolerance policy towards them.