What is the time frame of the embryo from which the cell is removed? How old is it in other words? How many cells total?
The procedure is typically performed on an embryo at the 4 to 10 cells stage of development. For the purposes of PGD one or two cells are removed. I would estimate that an embryo would reach the 4 to 10 cell stage at about 3 days after fertilization, but I don't know for sure.
For PGD, and PGD-comparable removal for stem cell research, normally no more than 8 cells (3 days post-fertilization). Most cells taken for embryonic stem cell research have been taken from blastocysts, which are a little further along -- apparently they're easier to keep going, but it looks like this group has figured out how to get comparable results from earlier cells.
I don't think there's any reason that a blastocyst couldn't survive cell removal just as well as these earlier embryos, but it hasn't been the practice to try to save blastocysts when they're being used to provide cells for research. If PGD is done for the purpose of selecting embryos to transfer into a patient, it has to be done by the 8 cell/3 day stage because results aren't immediately available, and doing the test later would mean the embryos were too far along by the time they could be transferred, to have a good chance of surviving and implanting.