So long as Day is:
1. Winning nearly 90% of his games
2. Bringing in the $$$
3. Not embarrassing the university with NCAA or "social" situations
He's not getting fired anytime soon. With a new AD coming in who likely won't be an Ohio State graduate, I'd say the chances of this remaining the focus within the administration is likely to continue.
The "3 question test" probably mattered more when Tressel and Urban were hired. 20 years of dominance probably lessened its importance within the AD office - for better or worse. Edit to add: I don't like it. I think it takes away the identity of the program to a certain extent, but at the same time, I think it's reality, and fighting reality is seems useless to me.
And the more I think about it, #2 is probably the most important of the 3 listed reasons. Ohio State LOVES to tell people how Ohio State's AD makes enough money to totally support itself. In the new era that starts next year with the 12 team playoff and 16 team Big Ten, it will be an even greater focus.