A week before my 11th statement cut, Cap One graduated my secured card - I was happy, of course! I have a QS1 with them too, and asked the live chat person if I could combine the accounts or upgrade to QS (I have no use for a Cap One Platinum with $500 limit and no rewards). The CSR got back to me within 5 minutes and said unfortunately, they could not upgrade to QS at this time, but please try again in the future. I tried a CLI on the website, but was shot down because I had received a CLI less than 6 months ago (I actually got one on my 5th statement, $200 - $500).
So I waited until after the 11th statement cut, and tried the CLI button again, got a 2 - 3 day message, and a response today that "credit limit increases are not available at this time for this type of account." It also mentioned too many recent applications (I have 12 HPs in the last 12 months).
I'll stop nagging Cap One for a few months, but I don't really understand what the "CLIs are not available for this type of account" message means. I run the card up to $450 or so every month and PIF every month. Only carried a balance one it once, 7 months ago.
You typically get that message with a secured card. It may still be in the process of converting.
Just give it a few more months....