Joe,
The solution given by you still works. I read your 2012 post and in 2016 when I faced the issue with my Samsung TV Model No. LA32S71BX/XTL, it worked.
After removing the back panel to access the side control buttons,
In fact I went a step ahead and actually opened the side control unit post disconnecting the 4 wire jumper (3 white, 1 blue) which on my model is separate for this section which controls, Menu, Source, Volume Up/Down and Channel Up/Down buttons only.
This specific part has a plastic buttons unit which we see on the outside and a Circuit Board which houses the buttons. These circuit board buttons are pressed when we use any of the buttons from the side panel, with the help of these plastic buttons. These plastic buttons are just push buttons and do not house any circuits on them. Hence post removing this part from the main TV, I unlocked the circuit board from these buttons panels (6 plastic locks that need to be released very carefully and gently). Post that I cleaned the Button Tops that are soldered on to the circuit board with a cleaning fluid. My TV is 9 yrs old and there was too much dust in this circuit part between the buttons and the circuit boards, this could probably be the one causing the Volume to go down on its own. After cleaning it thoroughly I ensured that the part dries up completely and then I reattached the plastic button panel to the circuit board. I reconnected back the board with the jumper cable, reattached to the TV unit and did a test run, it worked perfectly !
So while 1 option as mentioned by you is to disconnect the side panel buttons and only use the Remote Control for these functions.
The Option 2 is to clean the specific part with a little careful handling, as it does work perfectly after it. Hence getting to use the side panel and the remote, as originally designed.
Needless to say that the Option 2 needs careful handling and should be done at your own risks, Option 1 is quick and simple.
Thanks again Joe, I had nearly researched buying a new LED FHD, but your post has given the old LCD some more life now.