How long does a frozen box keep?

Endlessly.
Well, or until lightning strikes two data centers in different countries on the same day :)
Or until we run out of money to pay for server rent :)
And if without jokes: when any cloud box is turned off (it doesn’t matter, on the tariff for the user, on the tariff for data) - we automatically backup the entire box to two or three countries (free boxes to two countries, paid to three countries). And we keep these copies forever, never deleting them.
When the box is restored, we automatically deploy its state from the last backup, then after 24 hours the box is updated to the latest version.