GI 581 d is only rotating because it has a large moon that orbits in really close creating a tidal bulge mutch like on Earth but a bigger one just because the moon orbits really close. The moon though will eventually collide with GI 581 d for the same reason Phobose will collide with mars.
Don't forget [ame="http://en.wikipedia.org/wiki/Roche_limit"]Roche limits[/ame] if you want a plausible, albeit fictitious moon system around "d"... The ring system you placed around "d" really is a nice touch, because it hints that a moon recently suffered the outcome of getting closer than this limit. Depending on it's internal structure, Mars' Phobos will probably disintegrate in a ring system when it reaches this point, which is coming in a few million years. As for "GI 581 d I", it depends whether it is an icy body, a silicate or a metal-cored object.
Using data from your previous version, I get a mean density of 5351 kg/m3 ... Pluging that into the Roche limit equation, I get the following results:
A body of the exact same density would break the Roche limit at 17600 km of altitude above "GI 581 d" as it was in your latest release... A body of Earth's moon density would break up at 22700 km of altitude... An icy body, like a comet, would suffer the same fate at 53700 km above the surface.
Your existing "GI 581 d I" has a density of 4191 kg/m3 and would break up at 20134 km of altitude above the surface of "d". It currently orbits at about 62070 km above the surface, so there is a lot of spare space between it's position and the Roche limit below witch it would crumble.
As far as "falling" toward the parent planet, the rule of thumb is usually that if a tidally locked moon orbits faster around a planet than the rotational period, it will spiral down over time. If it's orbital period is greater than the rotational period, it will slowly move farther away while it's parent planet will very slowly loose rotational momentum, and spin slower on itself.
This is what is taking place with Earth's moon, which orbited a lot closer early in the Solar system's history, with the Earth spinning on itself in as little as 15 hours per solar day. Nowadays, the moon is moving about an inch a year away from the Earth, and both the Earth's rotational period and the Moon's orbital period slow down as an effect of this momentum transfer.
In the case of either your previous version or future version of GI 581 d and it's fictitious moons, the 21h orbital/rotational period of "d I" is much quicker than "d" either in tidal lock with the Gliese 581 star or with a sideral day of 96 hours.
So yeah, it would spiral down...