Yes, but it's supposed to. I found a nice chart on one of the glue packages at the hardware store. It was a matrix of gluing one material to another. Masonry and stone are best glued with epoxy. The interesting thing about this Gel epoxy is that it's the strong kind, but the manufacturer claims it cures to full strength in an hour. I let it sit overnight, then sanded off the excess and I wouldn't notice the hairline of the repair unless I look for it.
The important thing is that it be able to withstand the pounding. I seasoned the mortar and pestle this morning by grinding rice repeatedly until the powder was white. This took a bit of pounding and the repair seems to be OK.
My experiences with using the right glue are that the piece may break again, but never in the same place that that the repair was made.