They were finally yanked out by the roots, and regrew afresh so he could have them recoated at any time, Xavier may have connections that would allow it.
Do we have any good quality screencaps that show them extended in the "present" of DOFP?
They were actually cut off right at the aperture from his wrist. The cuts revealed a cross-section of the bone underneath, and Yashida looks like he's extracting Logan's healing factor from his bone marrow.
I don't have any screencaps, but the images I'm talking about are from the promos. We'll really just have to wait to see the movie to see if it's even addressed. Here's one: