I have two figures that don't seem to like to be on top of power discs - the first time I noticed this was with Finn, when using him with his costume-change disc. The base would flash red and not acknowledge the figure if it was seated firmly atop the disc, and would only allow the character to appear if I positioned it at a jaunty angle on the disc. Even so, the character would flash every once in a while, lose its costume, then play the animation as if I had just placed the disc under it, play the sound effect, and add the costume again.
I recently got Sabine, and have even less luck - I can barely use a power disc under her at all. I was using the Mace Windu team-up disc on a bunch of characters in TotR, and swapped out to her - no luck, the base flashes red and she floats in the air with clear blue coloring or the message dialog pops up with something to the effect of "Please place a Disney Infinity figure on the Disney Infinity base" or some such with any power disc under her.
These are the only two figures I have that have exhibited this behavior, though I can't say for certain as I'm not sure I've used all figures with power discs. Do I have defective figures of Finn and Sabine?
Addendum: I found this topic but it seems only tangentially related. The base is not on top of the console, or any other electronics, it is on the floor about 2.5 feet below the console. The problem only seems to be related to these two specific figures at the moment, as I've used the base in the same position with other figures and the same power discs with no ill effect. It happens whether there are a bunch of other figures scattered around the base or if they are moved away (again, using different figures, no problem no matter how close or far away other figures are). I have three bases at this point, and I'm almost certain I tried using others to no effect for the problem with Finn (I haven't tried with Sabine, but feel it would be futile).