It was essentially impossible for the Japanese to decipher Navajo code. There were fewer than 50 non-Navajo speakers in the world at the start of WWII, and they were all in the US.

Since the Navajo language was not written in any form, it would be impossible to learn it without being taught by a fluent speaker... you couldn't just go down to the local Japanese bookstore and buy "Navajo for Baka".

Not that it would entirely help. There was also an actual code available as well. True, it was a simple word substitution, but it added another layer of complexity to the equation.

Was it totally unbreakable? No, particularly today with high-powered computers. But for Japan in the '40s, with no basis to start from, it was.

edit: I was unaware that one Navajo soldier, Joe Kieyoomia, had been captured at Bataan. As /u/giveup21 points out, the Japanese did try to have him translate. Since he didn't know the code being used, it was essentially gibberish to him. He survived the war, after going through the Death March, torture, a voyage on a Hell Ship, and finally being in Nagasaki when the bomb was dropped. He passed away in 1997.