A rhizome is a rhizome. It's a reproductive underground shoot that develops during the growing season and if you lop one off and stick it in the ground elsewhere, it will produce a clone of the 'mother' plant. If the mother plant has contracted any virus/disease problems, the clone will most likely carry those problems to it's new location.
As long as the original plant material has been kept healthy I've heard reports of them being productive for up to 60 years. I'm sure there are variables that will push this number either way but as long as it's growing in a happy, healthy environment, I don't see why they couldn't be productive for many more years. Most of mine are around 20 yrs. old with a few that are 25.