This feature from The Forest, an Alpha stage game in development is a little buggy sometimes.
When the rabbit icon appears you should be able to pick it up but sometimes there is only one, or a limited range of positions you can be from the rabbit to pick it up.
It takes some repeated effort moving around the trap to find the sweet spot to pick up the rabbit when this happens.
Sorry about the frame rate. I didn't realize they changed the graphics settings with the last patch to provide for extremely dense grass and parallax occlusion which slowed down the frame rate with the use of the video capture software.