Enduring Magic says the ST rolls a die in secret. Meaning the player and the character both don't know what the final duration will be.
But CAN they know? It seems I should be able to cast an InVi spell to be able to discover how long a spell will last.
If I were to write it I think it would be the basic detect magic guidelines based on magnitude plus 2 magnitudes to determine when it will expire (I figure 1 magnitude would be able to read what duration setting it was designed at.)
Am I being to harsh/lenient? Should it forever remain a mystery by virtue of the Virtue?
I agree. With all the other stuff players/characters do to push the limits of magic, I don't see why you couldn't invent spells to peek inside the limits of your other spells to determine duration.
With that said, why not just come up with a breakthrough to take the die roll out of the SG's hands and put it into your own, thereby granting you the ability to know duration all the time without a separate spell?
I've never played out a breakthrough in-game and writing from memory (which isn't a strength), however the timeframes implied by the books for even a minor breakthrough is a decade, a major is a lot more, and a magus might only achieve a hermetic breakthrough once. The rolls needed, and the seasons expended imply to me that 1-2 decades is a reasonable timeframe for a minor breakthrough given the character will also be a character in the game.
Take it all with a grain of salt.