I have noticed something. Every time someone gets banned, they make an alternate account and ask why. This goes against the site rules and the moderators get involved. My proposal is that, when they log in after they were banned, they see a message. For example,
"Uh oh! You have been banned for 3 days due to spam". If that isn't an option, you could send them an email with the address they provided when they created the account. Anyways, that's my idea