This issue has to do with the fact that major grid lines overlap with the minor grid lines at the points with the major ticks. When you specify the 'MinorGridLIneStyle' as solid '-', and the 'GridLineStyle' as dashed '--', the dashed major grid lines are plotted on top of the solid minor grid lines and thus cannot be seen.
The ability to change this behavior of the grid lines is currently not available in MATLAB. To work around this issue, you can manually draw the solid minor grid lines using the PLOT command as outlined in the example below:
% generate a plot with the dashed major grid lines
figure
plot(1:10)
grid on
set(gca,'GridLineStyle','--')
axis([0 10 0 10])
% specify the minor grid vector
xg = 0:0.25:10;
% specify the Y-position and the height of minor grids
yg = [0 10];
xx=repmat(xg,[2 1]);
yy=repmat(yg',size(xg)');
% get rid of the elements in the xx vector corresponding to the major grid
% lines
xx(:,1:4:length(xg))=[];
yy(:,1:4:length(xg))=[];
% plot the minor grid lines
hold on
h_minorgrid = plot(xx,yy,'k');
