I believe they are forgiven after 7 total days, although I could be wrong. It makes sense to keep a log of bans on the competitive servers and have then eventually deleted. In my experiences (with teammates walking into my line of fire...repeatedly) I was lifted from the server's ban records and had little more grief.
UPDATE: More info found and posted below. Also this method of banishment applies to all forms of bans, including cheating, TK's, DC's and leaving early all are affected by the policy.
What happens if I abandon my match?
Updated: If you abandon a match then Classic Competitive will be unavailable for a period of time. The first abandon has a 30-minute cool down, the second is 2 hours, then 24 hours, and one week. If you haven’t abandoned for a week you would cool down by one level (for example, from 24 hours back to 2 hours).
Taken from here and reconfirmed in the community
Above information is for Official Valve Servers, Community servers are not a part of valve and contain their own rules. If you've come here looking how to reverse a ban on a surfing map server and the like, you are in the wrong place.