I'm not a crystallographer but is it not possible that this is a software issue and not a fault with the structure? Perhaps the XRD software is placing a single bond between atoms because the software has decided that the distance between the atoms is more likely to be a single bond rather than a double bond. Hydrogens are not usually detected in an XRD structure, they are placed in calculated positions based on the number of unassigned valencies and the geometry of the relevant atoms so the absence of two hydrogens would follow from the bond problem. The R-factor of the crystal structure solution should be poor if the structure is incorrect because the electron density map will not fit the hybridisation of the carbon atoms. You should ask a crystallographer about this. Also, you might do an IR experiment and look for a C=C stretch (although this might not help if there are other C=C components to your structure).

If the NMR data is clear and unambiguous then there are a limited number of possibilities: 1) There is a sample mix-up. 2) The single crystal selected for X-ray is different from the bulk material 3) The X-ray data is not very good

There is an assumption that the X-ray result is absolute but you can get poor X-ray data. You are looking at electron density and often inferring protons. What you look at is the electron density of the heavy atoms and deduce the bond type from the distance between the centres of the electron density and the angles of other atoms in relation. If you have disorder in the crystal or a weakly diffracting crystal you may end up with a poor structure. It would be worth checking with your crystallographer.

If the crystallographer is happy with their structure then I would look to the first two options.