AFAIK, no. Some registrars just don't want to take unnecessary risks if people are essentially transferring at the last minute, especially if unexpected and unwanted problems (knock on wood) occur.
It's actually even possible to transfer an expired domain name, but that's very risky. If a registrar says they won't allow transfer if within 7 or even 30 days before expiry, just look for one who's willing to take you in.