Check the e-mail for the e-mail address that you had on your UO account before the migration. You should find an e-mail with the subject: UO Subscription Expiration Notice that told you the account name and that it would expire in 7 days. If you can find that old e-mail, you should be able to roughly guesstimate when the account expired under the old accounting system.
I haven't received any expiration notices yet under the new system, so I don't know if they contain similar information. I notice that if you went into the account center last night to enter credit card information for an account that was "closed" (and that you thought you'd already set up to pay!), you receive two e-mail messages as a result. The first one has a subject line of "Bioware Mythic - Account Change Notification" but is utterly useless because it doesn't tell you which EA Account had a change nor which game account under that EA Account had a change nor does it tell you what kind of change was made. Utterly useless. The second e-mail you get has a subject line of "Bioware Mythic - Purchase Notification." It is slightly better than the change notification e-mail because it actually tells you which EA Account was used to make a purchase, what kind of purchase was made (e.g., UO 1 month subscription, and the purchase amount with taxes), but it also doesn't tell you which game account the purchase applies to!!
Hopefully, e-mail messages telling you that an account has expired will be more informative. However, I kinda have my doubts we'll even get such e-mail messages. So, if you're playing the 2 months off, 1 month on game, you may have to start manually keeping track of account closings and openings manually and hope and pray the decay period stays at 90 days. Also, I'm guessing that MAYBE once we have accumulated more history on this new account center, perhaps accounts that were open after the migration and then are closed will have more history on them so you'll be able to see when the account closed. Somehow, though, that just doesn't jive with what we're seeing so far. Account service reps may be able to see history, but I think the UI they built for players isn't that fancy or extensive and/or whoever designed it may think we have no need to see that information.
Anyway, good luck and I hope you can find the old e-mail messages you need.