First of all, there is no such thing as a permanent banishment. Account banishments always take a set amount of time after which the player can play again. I will assume that you are talking about the account deletion.
You can complain about every entry that is in your rule violation record and you have 60 days to do so since the day the punishment was issued. If you believe the punishment was unjustified for any reason, just click at the complain button at the corresponding entry and explain the situation. The same goes for account deletions as stated in the game manual.
Account Deletions
Account deletions are the most serious punishment in Tibia. They are only handed out if a player has violated the Tibia Rules
repeatedly and/or in a very serious manner. Please note that unlike other entries in the rule violation record, entries that result in account deletions do not have to be acknowledged by the account user in order to proceed. However, as with any other rule violation record entry, players whose accounts are about to be deleted are granted a 60 days complaint period.
Source: https://www.tibia.com/gameguides/?subtopic=manual§ion=support#punishments
Of course, I believe it rarely happens that a player is undeleted, as it's not in their business to delete players and lose customers. Therefore, if the account deletion is issued, they must have a strong proof that the punishment is justified. Mistakes do happen though, as we are only humans.