It's an implementation detail, so you can't really be sure unless you actually look at the implementation, and then it might still change between browsers or versions.
But my guess would be that the order remains the same at least if the object remains unchanged in the mean time. The reason for that being that there is some dictionary of properties, and as long as you don't mess around in that dictionary there wouldn't be a reason for it to return a different order. The order is not actually random, it's just not officially sorted in any particular way. So it's undefined rather than random.
Then again, as the answer you linked to mentions as well, the behavior is explicitly undefined, so don't rely on it. If you need a particular sorting, make it so instead of relying on undocumented implementation details.