Since thread was resurrected........
While not with Captial One, did have an issue with another bank and mobile telephone verification codes.
Spoke with CS and we quickly solved the issue; if mobile number in question is prepaid, pay as you go, or whatever else other than standard service, then yes, the codes often cannot and will not work. CS explained it has something to do with how the third party or whoever verifies mobile telephone numbers.
Have had the same "throw away" mobile number for years as part of a T-Mobile PAYG account that wanted for a "club" or "bar" phone. That is if lost or stolen wouldn't have my entire life.... It doesn't work with any request to have various codes (forgot password, complete transaction, etc...),so no longer bother.
Happily haven't had an instance where a transaction couldn't be completed.