When attempting to adventure without first opening the door:
You walk up to the Sinister Dodecahedron, itchin' to fight some holiday themed monsters, but you can't figure out how to unlock the front door. Maybe someone in Crimbo Town will know how to get in here.
When attempting to adventure after all the encounters for the day:
The ship appears to have entered power-save mode. All of the pod bay doors are locked down, and the Holographic Access Limiter refuses to open them for you. Try again tomorrow.
Each day, a new "verse" of "The Twelve Days of Mayhem" becomes available. For example, on day one, you may fight a death ray in a pear tree, then get your "verse" reward, a laser cannon. Then on day two, you may fight -- in order -- two turtle mechs and a death ray in a pear tree, then get your reward for "verse" two, a plexifoam chin strap. And so on. Including the reward adventure, verse one takes 2 adventures, verse two takes 4, verse 3 takes 7 and verse twelve (at the current rate) will take 79 adventures. This adds up to 376 adventures total for days 1 through 12 (364 combat, 12 non-combat).
After you defeat the death ray, normally the same message appears each day: "As you exit, the entrance hatch seals shut behind you and the entire ship powers down. Looks like it's going into power-save mode for the night." This only occurs if you have not missed any days. Otherwise, the ship will not shut down and you will continue adventuring. You will fight all the monsters for missed days, and get the non-combat adventures for each, before going on to the next day's monsters and non-combat.
Defeating CLEESHed versions the monsters in the Dodecahedron will not count toward that day's total (e.g., CLEESHing and defeating a Death Ray in a Pear tree will result in battling a second one).
This also applies if you ran away or were defeated.
After Modular, Dude (2), nothing is left of the Sinister Dodecahedron but a smoking crater:
Trying to adventure there afterwards yields the following:
The smoking crater of rubble that used to be the Sinister Dodecahedron doesn't look very festive. Or at all like a place where there would be monsters for you to fight.
Trying to adventure there using the Last Adventure link after Crimbo Town has vanished shows a blank page.
References
The combat adventures are all in reference to the Christmas song "The Twelve Days of Christmas," and in fact this event is starting twelve days before Christmas. Furthermore, all known (and presumably unknown) combat adventures reference what is received on the corresponding day. However, in most Christian traditions, the Twelve Days of Christmas start with Christmas day and lead up to Epiphany on January 6.
The Holographic Access Limiter refusing to open the pod bay doors is a reference to HAL 9000, from 2001: A Space Odyssey.
The Dodecahedron is a reference to Borg ships from Star Trek (specifically, The Next Generation, Deep Space 9, Voyager, and Enterprise series, as well as the movie First Contact). Borg vessels are generally simple geometric shapes, most notably cubes, but spheres are also common.
A dodecahedron is also a 12-sided figure, following the 12 Days of Crimborg motif.