Do you have an ODB2 code reader? If you don't, invest in one. You can get a good one for $40-60. I can't tell you how many times it has helped me narrow down problems. IMO it probably is a fault in the key FOB, not your 200s. I wish I knew more about how they work but I think it would be worth hooking up a code reader, remote starting your car til it shuts itself off and see if you get a code.