Paul Henney wrote:

The slowing of the tumble is actually more to do with a conductor (the
rocket) rotating and moving in a magnetic field (the earths) and slowing
due to hysteresis effects..basically an induced current makes the rocket's
tumble slow down over time.

That's pretty much what I was trying to say. The eddy currents
in the rocket's metal parts convert the physical energy into waste
heat. There are more details about this in various physics textbooks;
Halliday & Resnick describe it in their chapter about Faraday's
Law, but I'm not enough of a mathematician to figure out how to
apply their equations to a satellite.

There's a physics-class demonstration in which two metal disks
are rotated through the gap in a C-shaped magnet. The serrated
disk spins easily, while the solid disk is rapidly slowed by
the induced currents.

--Bill Thompson