Interestingly, Wikipedia disagrees.

For a radix of 10, there is thought to be no number with a multiplicative persistence > 11: this is known to be true for numbers up to 10 to the power of 50.

http://en.wikipedia.org/wiki/Persistence_of_a_number

I guess the problem is that when you multiply lots of digits together you become increasingly likely to end up with a 0 digit somewhere.