This story-identification question was asked on June 16, 2013; I answered it on July 1, 2013; and my answer was accepted today, April 23, 2021, almost 8 years later. Is this a record?
Looks like it. The previous record was about 7 years.
Our overall record of over 8 years hasn't been broken, though.
Here's the top 15 at the time of answering (yours isn't in SEDE yet).
I created the following SEDE query to test this:
SELECT a.Id AS [Post Link], a.CreationDate AS [Answer Time], v.CreationDate AS [Accept Time], CONVERT(varchar, DATEDIFF(s, a.CreationDate, v.CreationDate) / 86400) + ':' + CONVERT(varchar, DATEADD(ms, (DATEDIFF(s, a.CreationDate, v.CreationDate) % 86400) * 1000, 0), 114) AS [Difference] FROM Posts a JOIN Votes v ON a.Id = v.PostId WHERE VoteTypeId = 1 AND DATEDIFF(s, a.CreationDate, v.CreationDate) > 31557600 ORDER BY DATEDIFF(s, a.CreationDate, v.CreationDate) DESC
The top 5 results are as follows:
|Answer||Answer Time||Accept Time||Answerer||Questioner||Difference|
|What evidence supposedly supports Tau as related to the Necrontyr?||2012-08-31 23:22:28||2021-01-08 00:00:00||Thaddeus Howze||AncientSwordRage||3051:00:37:32|
|Gaiman's Hamnet||2012-07-20 21:56:52||2020-09-25 00:00:00||dlanod||Andrés E. Caicedo||2988:02:03:08|
|Why Was the Burrow Burned Down in Half-Blood Prince?||2012-05-31 07:48:43||2020-05-06 00:00:00||Tango||Slytherincess||2896:16:11:17|
|How does Bruce travel from The Pit to Gotham City?||2012-08-18 18:21:59||2020-06-11 00:00:00||Jack B Nimble||Wipqozn||2853:05:38:01|
|How do the mutant levels correlate with the mutant classifications?||2011-11-23 02:58:50||2019-09-10 00:00:00||Thaddeus Howze||Jack B Nimble||2847:21:01:10|
Your difference actually comes in at roughly 2997 days 20:12:45 and so when SEDE updates it will come in second overall but the top one for story-identification!
A markdown friendly version of the query can be found here if anyone ever wants to add to this.