Are you trying to use a 3rd party remote or Olympus' own? I have an E-M10 and bought one of those programmable ones on eBay. I never got it to work; I concluded that the molding around the connector prohibited me from inserting it completely. I bought a second one, different type, still 3rd party and of the classic Olympus type. It works fine. BTW, for those advocating the wireless app instead of a remote, the app is great but has its limitations in that the wireless signal from the camera is very short range and you can lose connectivity if your camera is more than a couple of feet away. This imposes some constraints that a remote can solve. That's why I bought one.
It could be a bad contact in the remote, assuming that the USB connection works in other respects. I have two eBay remotes and they work fine with my Pen cameras and E-M1, so the logical culprit would be the remote. It's pretty simple to open the casing to check that all is in order inside, so I'd have a look at that in the first instance.
Here's a photo of my RM-CB1, which I assume would be similar to the USB version, and you can see a sliver of plastic between the top and middle contacts to lift the top contact, which I had to insert because mine also played up (can't now remember exactly in what way):
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Hmm, thanks for this post, I bought a timer remote cable a few years ago for taking meteor showers and never could get it to work.. was so cheap I just forgot about it.. will check the connector, although that was for the EM5 and I have EM1 now, not sure the setup is the same