Derivative of signal with missing samples
See Smooth noise-robust differentiators. While Pavel doesn't address your specific problem there, he and I corresponded about a similar "missing samples" problem earlier this year, and he has some good ideas that you can try. In particular, he recommends polynomial approximation in the region of the missing samples. In addition I'll mention that if you use Neville's Algorithm you can guarantee that the polynomial passes through your "good" sample values. You can find Pavel's contact info in various places on his Website.

Greg Berchin