*Keys are temporarily exhausted for this product*

That's really unfortunate... Many of us faced this problem before and we can't know if Humble will add more keys. Chances are actually really low. I'm not sure if contacting their support would work but who knows.
Yes you will get suspended for not activating your won game plus you will end up with unactivated win so the only option you should go for here is to mark the giveaway as not received after 7* days. This is definitely not your fault that the game is not available from where it was purchased at. Giveaway creator may get you a new key if he/she feels so though.

If I understood you correctly, you had a gift activation link as a prize, but you are temporarily unable to claim the key there. I encountered something similar a few months ago. In my case, I warned the author about the issue and notified him that I would not mark the gift as "received" until the key appears on that gift activation link (it was the HB store). Sometimes I went to HB and checked the situation. After a couple of weeks, everything was resolved positively. :)

I don't know if there is any point in suggesting something like this, but you can try contacting support. Previously, HB sent a notification to the mail about the replenishment of the keys for the game you needed. I don't know how things are with this now.

Or - if you don't want to bother with this - try to negotiate with the author of the GA about replacing the key or - radically, but most simply - about deleting the GA.

You can't activate the game, so, no, you won't be banned.