According to this Reddit thread, the pre-built probe for this mission has two probe cores: the obvious Stayputnik core on the top, and a second HECS(?) core hidden between the monoprop tanks and the batteries:
Image from Reddit thread linked above, presumably by Reddit user djdupre.
To stop the power from draining too fast, you'll have to hibernate both of these probe cores.
(Ps. I'm marking this answer as Community Wiki, since I don't really feel justified in taking credit for just quoting someone else's answer from another site. I can't even really test this myself, since I don't have the expansion. The screenshot does appear to confirm the existence of the second probe core if you look closely, though.)
(Pps. There's another Reddit thread that says the same thing, and notes a few other issues with the mission as well.)
NOTE: Here is the image showing the HECS that you need to hibernate. It is located below the GRAVMAX Negative Gravioli Detector. This image was taken on the land site before launching: