I see the fairy tale about resting a razor is back Sick of that Bull-Chunder being banded about as gospel. Can't wait for the Thumb stopping to be vomited back into life.

Stropping post shave is a good way to clean and dry the razors edge.
A light stropping before a shave serves the same function.
When a razor starts to dull, you then strop the razor more pre shave.
When a reasonable amount of stropping fails to work you can then turn to a pasted strop etc.
When pastes don't work you can then turn to a hone to refresh.

As to when to strop, this has to be a users choice because he is the one getting the feed back from his razor. You may deicide after a shave that the razor didn't perform too well. This will determine the amount of work on the strop/hone will be required for the next shave.
Yes razors can go for many shaves without stropping if kept clean and dry. It has to be born in mind that the strop fills a multi role in razor care.

PuFF