This question is kinda weird. I know nothing about the system so im not going to really know how to figure out how they broke a rule. but if you knew how to find out if they broke a rule you could set a cookie when a rule is broken to expire in 3 days. Granted they could delete the cookie but they might not hehe.
If you want to do it sophosticated like youl lhave to database the users and then put a date int he database when they were ban and dont let them log in til past that date.
If that helps i dont know but i have no idea how you are keeping track of users, how you know if they are logged in, what verifications you are using. And by setting that all up id assume you would come up with a solution? but if you want to elaborate more on the design of the community then maybe someone could give you more help, question to vague.