Sensei, the cypher we both use is a simple substitution one. Since we solve message by measuring the frequencies of letters to break the substitution, running it through the machine three time should not prevent us from decrypting at all. :p
This entirely true, running a simple ciphered message through a simple cipher again is the same as just using a different simple cipher, and the resulting code can be cracked the same way it normally would.
However, Arstotzkan code breakers are actually not terribly clever, or maybe too clever. When a Moskurg soldier decrypts a message with one code card, they usually forget to turn the Tiger's Whispher machine off before going to the second and third. The resulting second and third messages have been interpreted as some kind of super cipher, even though they apparently decrypt to the same thing. This, combined with Moskurg soldiers' penchant for just not following orders in lieu of instinct and bravado, has led to the incorrect assumption that Moskurg is using some new cipher which cannot easily be cracked, and are actually following orders from their cleverly hidden double cipher. At this point, Arstotzkan code breakers open up a bottle of Five Star, and suggest cryptology theories to explain the secret Moskurg code, which get worse and worse as the bottle empties.
Objection to the Unreliability of the Hippo. We can just make sure soldiers dispose of the tubes every 30 shots.
This would probably make it more expensive, in effect, due to manufacturing multiple hippos per user. However, much of the damage has been done at this point in that soldiers are afraid to use the thing until you change it. It also still fails in general in bad weather.