If you use the suggestion from my first reply, about setting up a playlist in iTunes with the songs you want on the shuffle, and syncing that playlist to the shuffle after the Restore (by selecting it in the shuffle's Music tab), then you will be using automatic syncing.
If you currently dragging your songs to the shuffle in iTunes after doing a Restore, then you are using Manually manage music.
If you eject the iPod and leave it connected, then the light should be solid and it should turn green when fully charged. It's possible that the battery is becoming worn out through use, and that is why it does not show completely charged, but I don't know why it does show green (for one time) after you do a Restore. If you do a Restore and get the light to "go green," set it to Manually manage music, disconnect it, and immediately reconnect it, is it still solid green or does it become solid orange (since it's no longer immediately after a Restore).
Normally, the shuffle battery should become fully charged within three hours (from empty). It may be working the same (in terms charging and available play time) whether it starts out orange or green. If you are curious, you should time it playing songs continuously at the same volume level, to see if the play time is significantly different.
It certainly might be the battery since I've used it every day for 3 1/2 years. Thanks, I will try your suggestions this weekend.