Just log out and back in again :-)
http://www.gog.com/forum/general/2014_drmfree_big_fall_sale_8b1f1/post386

If you see that your first stamp is gone, just click it again and the second should be unlocked.

Log out, then log back in.

I had the same problem and this fixed it, for now.

Logging in and out doesn't really fix it:
https://www.gog.com/forum/general/witcher_2_stamp_collection_gamification_thing_seems_to_be_broken/post25

I logged out and back in again, still can't unlock the second stamp.

But you did unlock yesterday's stamp?

Thanks for the very quick response! I just figured that out and was coming back to update my post and you had already responded. I logged out and logged back in to find that I lost my first stamp too, but then when I clicked on the first one again they both appeared. I predicted something like this would happen after my first stamp yesterday so this caused me to have a knee jerk reaction of anger. I really do appreciate the free game offer but I think there might have been a better way to go about this. Something tells me there is going to be a flood of emails to GOG after this promotion is over. Hopefully there will not be any more problems like this.

My problem is already fixed. Two ticks right now even if I log out.