Pardon us if some portions of this post sound a bit redundant. Nonetheless, we hope this information will in some way help.
It is our understanding if you are the current registrant and you have inadvertently let the name pass the renewal date far enough for it to enter the redemption phase, you will have to pay the fee to redeem the name. To our knowledge, GoDaddy currently charges $80 for this redemption fee [someone correct us if this figure is wrong].
In light of a prior post, which suggested you bid on the name at snapnames (typically a $59 minimum bid...?), you may as well just pay the full $80 direct with GoDaddy and be done with it, being there is only a small difference in cost. You will then have your name back and though a bit costly, lesson learned. Just remember moving forward to renew prior to the actual date.
However, if you are "not" the current registrant then unfortunately, you will in fact have to wait for the name to be released to the open market once again (as also mentioned in a prior post). Typically 30 to 45 days is the standard, though it can fluctuate outside of those time frames. At this point, you may want to use snapnames or some other registrar to help you get the name. Even GoDaddy, which will charge a smaller fee (especially since it is currently registered with them), can help try and obtain the name for you once released again. This method may be best if you are not the current registrant.
At any rate, if in fact you "are" the current registrant - another option you may want to try is contact GoDaddy Customer Service direct (480-505-8877), if you haven't already done so, and speak to a Customer Rep to plead your case. In doing so, ask them if they can wave some or all of the redemption fee as a one time courtesy. Tell them the delay was out of your control. We have recently heard GoDaddy have been willing to at least reduce the fee, so it couldn't hurt to try. Just remember to exercise some courtesy when speaking with them. Demanding they waive or reduce the fee will not benefit you and will only work against you. If the name is just too good to wait, any cost is worth it to get it back, but it can't hurt to try and save a few dollars in the process. Just a thought.
Sorry for the long post. Best of luck. Keep us all posted...
-Regards