We had an a Line 6 Flextone III come through for repair, customer complaint was that the presets were turning themselves off after about a minute of play, this resulted in a volume drop similar to that experienced by some users on this thread. The preset selection LED would stay illuminated but the actual preset values disappeared.
I flashed the firmware and the problem is now gone, the amp also seems to have more overall volume.
Anyway I can confirm that flashing new firmware can resolve these issues (at least in my case).