I do not understand from the scenerio above... if you asked the County Administrator for a reason?
It sounds weak if a possible employer asks you why...and you are unable to demonstrate that you asked the same question of your employer and apparently have not received any answer.
If he/she is unwilling or able to provided you an answer, I would make a plea to your ex employer... that without an answer you are missing employment opportunities.
Will he/she provide and answer. Would he/she be willing to respond to potential employer that he would re-employ you under a different board?
How about a positive statement by your ex-employer that there were no "for cause" reasons! Further, a positive statement that you were an ethical, upstanding local government manager working in an "at will" employment situation.
Finally, if your past employer will not help, it is time to come up with your own answer, even if it is a guess. Provide your response by saying I was not given a reason but if I had to provide an answer it would be.....?
Saying I do not know leaves too much to the imagination.