JefWright: I actually rather like the original magic remote. I've never had a problem with it but I've replaced it with a $20 Harmony (200 I think) because I wanted to control more appliances. The Harmony key layout is not as user-friendly.
For the record, I believe the oily substance is a plasticizer added to a (probably pvc) membrane to allow it to flex. It migrates over time and contaminates the contact area. Elevated temperature and pressure seem to increase its rate of migration.
One could try soaking the membrane in a solvent for a while to liberate any free plasticizer near the surface. If you don't know what the oil is, don't ingest it. It quite likely contains phthalate esters which are banned as endocrine disruptors under Europe's RoHS legislation.
I think you may be correct, except the keypad is probably silicon. I just googled and it seems that even silicon is doped with plasticisers. My remotes worked 100% after the first wash but only lasted a few months. After the second wash, only some keys worked and that lasted a few weeks. The third wash was done by dishtv and still, only some keys worked and it worsened within a few weeks. So there is something else breaking down inside. Quite possibly the washing and touching is causing damage to the pcb by static electricity.