I've created a logo in Illustrator and saved it as an AI. When placing it in an inDesign document, one of the objects in the logo goes to the back and refuses to come to the front. If I copy and paste the logo from Illustrator into Indesign it's the same issue. If I use a different color for the object in the logo and bring it in then it works but if I try and change the color back to what I want in inDesign it automatically sends it to the back and refuses to come forward. If I recreate the Logo in inDesign and use the specific color I need, it sends the object to the back. Also, there's no transparencies or blending modes applied at all.
Could it be that the file is set to Overprint?
Ahhh yeah. Of course. It was set to Overprint.
Is there no way to retain layers in Overprint or is it just a bug?
Layers and overprint are not incompatible. The stacking order will remain whatever you've set, but overprint means just that, the color will print on top of any other object behind without knocking it out.