I don't know if it's hurting your credit profile sitting there dormant, but I can share with you a similar story with a Capital One card.
About 10 years ago, I operated a small business and had significant CC charges - up to $60k in one month on an Amex. I also had substantial credit lines open with BofA, Citi & Chase ($10-30k). I applied with Cap One and was given a business card with a credit line of...$500. It didn't have a fee or anything so I just let it sit there, maybe used it to buy lunch once every few months, but didn't really use it.
It went like that for a few years, then I closed the business and returned to graduate school (around 2007). I didn't need for large credit lines any more, and of course my income went to basically $0 for a few years. The other CC companies reduced their lines, and Cap One declined to issue a new card when the old one expired. It was extremely weird, the account still had a $500 limit, but they didn't issue a card with an updated expiration date, so there was no way to use it. Again, I let it sit there.
I finished school in 2009 and the company I was set to join went into bankruptcy. The job market was extremely difficult at the time (it wasn't that long ago, I think most people recall), and it was almost 2 years before I found full-time work. I tried to keep up with my other credit acounts, but it was impossible and they went into charge-off. Still, this Cap One account sat there dormant.
A couple of years ago, I landed a great job, settled all my charged-off accounts and started fresh with my credit profile. The only thing I had remaining through all that time was a Citi business card which is a non-reporting TL for me; the limit used to be much higher but they chased it down to $1k and left it there. After settling all the charge offs, I called up Capital One and asked if they would issue a card for this old account that had been sitting there for years, and they said yes! I also opened a secured card with Cap One around that time. I started making on-time payments and slowly gardened the accounts that I had. About 6 months ago, I applied for a QS1 card with Cap One and they gave me $3k (now $3.5k with CLI), and in January I applied for a Venture and got $5k, all instant approvals. I closed the secured card at that time, and got a CLI on the old business line from $500 to $1500. I can't help but think that the positive history with the old account had a lot to do with the approvals. There's no doubt that it is my oldest CC line by a mile (the Citi Business card I have is non-reporting TL).
So, given where you stand now, if it's zero balance and doesn't have any fees, I'd just leave it. At some point, Cap One might be willing to re-open the account, and as it sits there it will age and add to your AAoA.
