I realise this comment is probably an exercise in pedantry, but as Latin is an exact language, I feel justified in raising it.
Since his hope is becoming very small, let him confess that he commanded those two men not to do it.
Cum fiat spes illius minima, fateatur se imeravisse istis duobus ne id facerent.
First of all let me agree that the answer is correct, and the sense is obvious, but what is the subject of fateatur? Isn't it the subject of the cum clause? If so then it is the hope, not the man with the hope that is doing the confessing. My answer-
Cum fiat spes illius minima, ille fateatur se imeravisse istis duobus ne id facerent.
A link to a similar problem in english: http://www.worldwidewords.org/articles/ar-pos1.htm