Tom Swanson over at Swans on Tea calls this sort of ploy "writing press release checks your physics can't cash." It's a device, after all, and a macroscopic one at that, requiring an ion trap and the application of electric and magnetic fields - a drawback that Li acknowledged to New Scientist: "You need to figure out a method to make a laboratory that can survive in the heat death of the universe."
Swanson has a point. An atom or molecule might make it, but a lab? That's a tall order. I mean, you might as well just say you can use the spacetime crystal to build your own TARDIS. (*cough*)
Oh, and in order for such a clock to keep time, one needs to be able to measure the periodic oscillations by shining a laser onto a particular ion, and that's going to mess with the accuracy big-time. "It would be like counting a wheel's rotation by painting a spot on its rim and counting how many rotations you have," Swanson grumbles.
And remember that there's always going to be uncertainty associated with an ion's location because HEISENBERG. As Swanson says, "Go ahead and blame me for being the reason we can't have nice things that are perfect and last beyond the heat death of the universe."