I'm not worried about a thousand years into the future. Most electronic data won't be accessible in 50. CDs in perfect storage conditions may last 30 years, but will you be able to get a device to read them? NASA has tons of data from the viking and voyager spacecraft sitting on magtapes that can no longer be read because they've decayed so much.
In a modern society, if you want data to survive, you must have a system in place to constantly refresh the old data to new media. You also have to convert file formats as well. It's a major issue, and one that is not really being dealt with even with the resources of FedGov.
Fired clay tablets work. It's not trivial to update the files, though.