Traditional prohibitions are set in the 2 x 2 grid, i.e. don't allow Attribute 1 level 1 to show up with Attribute 2 level 1. Alternative-specific designs are where we knock out an entire row or column, i.e. don't allow any level of Attribute 2 to show with Attribute 1 level 1.
So, the initial way I thought to do this would be to collapse A and B down into a single attribute with 4 levels:
Then you could enter in the prohibitions as usual and prohibit all levels of C from showing up with levels 1-3 of the new, bigger attribute A/B.
Then I re-read the post where you say you set the prohibitions, so I gave it a whirl in the Advanced Prohibitions tab to specify a complex within-concept prohibition (I've never tried it there before). There is a warning that comes up that says "Although this is allowed, such prohibitions may make it difficult for the designer to find proper alternative-specific designs." But, upon clicking to proceed, I indeed get a message that the task could not be generated according to the constraints.
So, the likely explanation is that the designer algorithm has some issues with interpreting these types of prohibitions, and it's more of an internal code issue that really a tough design issue. So, I'll step back and go with my initial suggestion of collapsing down the attributes.