You mean the foot plate (closed or open toe) comes off the foot ?
Indeed When I first looked at mine I thought it was plastic because of the look of it but it isnt and it is meant to be removable so you can attach the open toed plate if you want.
Check you have both the nubbles on each side of the Plate/foot engaged into the holes/depressions properly ...
If it continues to fall apart take it back to your dealer or ring Janome customer service, explain the problem and they will probably exchange it for a new one.
Check out a janome vid of how to attach and use the foot, which shows exactly how to change the sole plate and engage the foot to the machine.