Well, duh.. I should have taken photos, but I didn't.
Recently I acquired a fourth player for various uses around here, and the Rio Remote that came with it never worked. Well, okay, popping the battery out and back in again would sometimes get it to function for about 10 seconds or so before it went "dark" again.
Anyway, just now I decided to see if it could be repaired. Fiddling with the battery contacts through the battery slot proved futile, so down to the workshop it went.
First, I peeled back the foil "Rio Digital Audio" sticker from the backside, about halfway, and scotch-taped it out of the way. Some citrius solvent made instant work of removing the gummy adhesive left behind.
Next, a nice shallow 5/8" forstner bit on the drill press was applied to the backside of the remote, centred about an inch or so from the bottom of the remote. This revealed the innards, with near full access to the contacts and solder pads for them.
The first repair attempt was to bend the contacts to more firmly press against the end and face of the button battery. Very easy to do this through the hole.
Instant success! Works great now. I cut a matching "button" from some scratch plastic to fill the 5/8" hole, and applied thin double-stick tape over the back of the remote to secure both the patch button and the Rio foil label in place. Looks nice now, too!
So, if you've got a failing remote, don't despair -- ask for repair! (okay, so I couldn't resist the rhyme).
Cheers