Nokia 5610 has a slot just near the camera. When the cover is placed, a snug will push in to the slot. Then only the memory card will be detected. This feature is there to make sure that the memory card is detected only when the back cover is placed perfectly..
Mostly your problem is that. You can press the back cover near the camera to confirm this. Then you can see the memory card is being detected and when you release it will be gone.