if this is authoritative https://bitcointalk.org/myips.php I would say that the IP address is remembered only for 30 days. at least that's how I see it for my account.
Thank you. I was looking for the link to find the correct retain time. I was in a doubt if that was for 3 months or 6 months. That's why I did not put a time there.The most recent comment from theymos I could find on this:
There's now an option in your account settings which will allow you to reduce retention of your logged IPs to 3 months. You should only consider enabling this if you've staked a pubkey in the thread and you're sure that your account email is correct. I'm not sure if 3 months is enough to respond adequately to all abuse; we'll see, and I might change it later or perhaps restrict it based on rank.
So, it seems that the shortest possible retention time for the full IP address is 3 months. I'm not sure if anything has changed since then, but I see the same information also on the "About privacy" page:
I assume https://bitcointalk.org/myips.php shows only 30 days of data due to security reasons.