Unfortunately, the website will not be updated in the near term, so this problem will persist. This isn't as clear-cut a problem as I originally thought. I was having problems with my account. Popup configurations were pretty much working for me when I use another account I have.
Is your service public? Can you post the URL here? Maybe it's something specific to your service.
As I mentioned before, are you sure you saved the popup configuration (clicking the button at the bottom of the panel once you make changes)? The menu button to save back to the service item will be grayed out if you didn't.
It's possible that the popup properties are getting saved to the service, but they're getting overridden by the current web map that contains it. You don't actually need to save a web map to author the popup properties for a service. Find the service in My Content and open it. You can then modify the popup properties and save them back to the item, then just discard the web map.
Here's what I suggest. Directly open the service in a new map and see what how the popup properties are configured. This will rule out the possibility that your existing web map is overriding what's set on the service. If they look correct, then all is good. If not, you can correct it and save the changes back to the service item. You can then go to your existing web map and remove the layer pointing to the service and add it back again. Explorer Online also has the option to reset the popup, which should revert to what the service defines, I believe.
Hope this helps,
Mike
