Mathworks states in their description of corrcoef,
"R = corrcoef(X) returns a matrix R of correlation coefficients calculated from an input matrix X whose rows are observations and whose columns are variables."
To be meaningful in such correlation calculations, variable values in your two variable vectors within the same row should be matched observations, that is, values that were made in the same observation. Therefore you shouldn't eliminate a NaN in one variable without also eliminating the corresponding entry in the other variable even if it isn't a NaN. As a corollary to this the two variable vectors must therefore remain of the same length.
If you don't maintain this correspondence between matching observations, you will obtain nonsensical results.
Roger Stafford
