Yes, it is rounding. datenum('01-May-2014 15:00:00') is 735720.625 so anything that does not reach .625 after whatever internal rounding will convert to hour 14. Experimentally I find that the breakpoint is between 735720.625 * (1-35*eps) and 735720.625 * (1-36*eps) which is somewhere around 6.8E-10 seconds
current_tim=current_tim+datenum(0,0,0,1,0,0) ;%adding one hour in each loop
Remember that datenum(0,0,0,1,0,0) is going to be expressed in floating point as fractions of a day, not as integral hours. As 1/24 is not exactly representable in double precision floating point, the double precision representation of 1/24 is going to be either a hair less than the true 1/24 or a hair more than the true 1/24. When you start adding together those hairs, you are going to end up with values that are not exactly what they should be algebraically, leading to problems like you saw.
Try
start_tim=datenum(datestr('01-May-2014 00:00:00'));
for k=1:24*7
current_tim = start_tim + (k-1)/24; %k hours
datestr(current_tim)%checking
hour(current_tim)%checking
[out] = YourFunction(theta_pre,weaData,current_tim,I(k));
end
