Start something like
If the above is false (0), you can use the previous result with linear interpolation; you've proved there is no gap of 4 hours or more in the data.
OTOH, if the above is true (1), then you need to find which days are those--this can be done by retrieving the individual elements of the logical vector
From this index, return the year,month and day of those elements and then remove those days from the original interpolated series. (If you remove and then re-interpolate with retime, it will just fill in all the elements again so you have to remove them afterwards).
Those days should be removed from the interpolated result above as Walter showed.