[kakwa_]

The tapes themselves could last 300 years (or, for more realistic common needs, around 30 years).

However the tape reader/recorder will probably not last that long. These things need special care (don't forget the cleaning tape every other month) and can act a little weird when the mechanical parts wear down (or even before in many cases).

The Ultrium LTO standard states that a tape recorder for version N must read/write N-1 and read N-2. Given that there is a new version around every 3 years, it gives you around 10 years of strong guaranty on your capacity to actually recover your data.

To properly manage data on a longer period you need to migrate the data to a new media. In fact, the problem then became mostly organizational.