The way the system works, it is 100% possible to get a permanent ban for something minor. There are 4 punishment tiers:
1.) 10 day chat restriction
2.) 25 day chat restriction
3.) 14 day suspension
4.) Permanent ban
Whenever you get punished, you move up the punishment ladder, regardless of how minor the offense may have been. This means that each punishment gets harsher and harsher until you reach the permanent ban, and the reform card for your 14 day ban specifically says that your next punishment will be a permanent ban should you continue with your behavior. When you reach the permanent ban step, you're essentially showing Riot that you're unable or unwilling to change your behavior, thus Riot no longer wants you to play their game.
If you want to contest your punishment, you can submit a ticket to Player Support, but if you have gone through the above punishment tiers, then unfortunately you're out of luck as Riot doesn't overturn bans that weren't given in error.