I am very happy to report that the Mystery of the Missing Bunny has been SOLVED. And by none other than Emma herself!
After two days of searching and driving myself crazy, I finally gave up this morning and decided Bunny would simply turn up when he turned up. Wouldn't you know, that was all it took (isn't that the way it always works). Not too much later, I heard Emma give a delighted squeal of "my bunny!!" from her room, and sure enough, there he was. I guess he was hiding all this time in a basket of Build-A-Bear clothes. I have no clue how or why or by whom he was put in there, and what's more, I could have sworn that I thoroughly checked that very basket... but it doesn't matter. The important thing is that Emma and Bunny are happily reunited at last.
Don't ever leave us again, Bunny. We missed you so.