Just keep track of where all elements are NaN, and replace their sum with NaN after using nansum. You should be able to adapt this example to help you, it sums along each column:
>> A = [1,2,NaN,NaN;3,NaN,4,NaN]
A =
1 2 NaN NaN
3 NaN 4 NaN
>> B = [6,7,8,NaN;9,NaN,NaN,NaN]
B =
6 7 8 NaN
9 NaN NaN NaN
>> C = nansum(A+B,1)
C =
19 9 0 0
>> C(all(isnan(A)&isnan(B),1)) = NaN
C =
19 9 0 NaN
