The batteries that ran out were for the locator beacon.
If the actual data storage for the recorders is in Flash memory then it should last a few years, at least assuming no damage to the IC packages letting in water or from mechanical stress. The AF447 recorder was recovered after nearly 2 years, for example, and cold water would tend to slow down leakage of data from the flash cells.
I do agree about the remote chance of finding it though. Someone may stumble onto the wreckage later, but as you say it's also possible it will be covered by a layer of silt and therefore eventually invisible. And it's suspected that the voice recorder wouldn't tell us the original cause anyway since it would not include the start of the flight when the unexplained maneuvers started. Similarly the data recorder may also just include running out of fuel at the end followed by descent :(
Hence the decision not to spend another $100M on an uncertain search seems understandable.
Biting the hand that feeds IT
