A unique "non-evaporation" phenomenon, i.e., the unusually slow evaporation process of sessile microdroplets on self-assembled monolayer (SAM) surfaces, is reported. It has been observed that only droplets containing a certain proportion of a volatile and a less-volatile component undergo non-evaporation, which is characterized by hours-long existence of the droplets maintaining constant contact angle, contact area, and volume. We propose that for alcohol-water binary mixtures on SAM surfaces, the highly orientated and closely packed hydrophobic 1-decanethiol molecules induce a concentration gradient of alcohol in water, with a higher concentration of alcohol near the SAM surface. Initial evaporation of the alcohol (more volatile) increased the contact angle until the establishment of a new composition, which contains a strong hydrogen-bonding network among the water molecules in the presence of the alcohol alkyl chains. There is a lessened tendency for the alcohol to evaporate in the presence of a concentration gradient due to such interactions, which results in the observed "non-evaporating" phenomenon. This type of unusual evaporating profile was not observed on conventional substrates, such as polycarbonate sheets and microscope glass slides modified with alkyltrichlorosilanes.