While it should not be the passenger's responsibility, it befalls the passenger to track the issuance (or reissuance) of an e-ticket. If you do not see your new e-ticket at 5 days, call in.
It is an absurdity that in this day and age, tickets and most particularly reissuance of tickets is not close to immediate. AA tickets issued in the UK (where the CVV problem arises) are generally handled either immediately, e.g. you will have an e-ticket confirmation by the time you hang up, to the next business day on those rare occasions when AA's "rate desk" must look at the ticket (something which occurs much more frequently on BA due to the lack of automation of its front line pricing).