http://www.michaelshell.org/gadgetsandfixes/keypadsiliconeoil.html
So I guess these silicone button pads actually "sweat" silicon oil over time. Apparently this is a thing with the button pads on remotes like this (planned obsolescence maybe?). The fix is pretty simple, just clean the pads with dish soap and an old toothbrush (that is not going to be used again of course). Getting the DirectTV remote apart can be a bit difficult though - fortunately somebody put a video up showing how: