The answer is ... it depends.You were expecting that, right? Especially if you're moving mogrts with assets from one machine to available in many.
When mogrts include assets, those assets need to be handled correctly, as they're placed in the comp or whatever over in Ae. I've made some mogrts there, and a couple did this behavior and I had to figure out how to fix it, but sadly, the gray cells above my glasses haven't retained that specific little detail among all the other things I've been trying to retain in working in Ae. Ahem.
I think asking this in the Ae forum would get a quick answer. Although probably someone around here has more of their Ae work memorized than I do.
Had the exact same issue, I had a background stock footage that wasn't being exported in the .mogrt file I was exporting.
The fix for me was renaming my background footage to a reasonable length. The original file name for the footage was ridiculously long (171 characters).
If you're wondering what the file name was it's: "videoblocks-animated-closeup-fireplace-and-gifts-in-the-christmas-socks-on-bricks-background-luxury-and-elegant-dynamic-style-template-for-winter-holiday_hyil2bhfp_1080__D"
Changed the name to "background" and it worked like a charm.