We investigated how the stability of aqueous argon surface nanobubbles on hydrophobic surfaces depends on gas adsorption, solid-gas interaction energy, and the bulk gas concentration using molecular dynamics simulation with the SPC/E water solvent. We observed stable surface nanobubbles without surface pinning sites for longer than 160 ns, contrary to previous findings using monoatomic Lennard-Jones solvent. In addition, the hydrophobicity of a substrate has an effect to reduce the requirement degree of oversaturation on water bulk. We found that the gas enrichment layer, gas adsorption monolayer on the hydrophobic substrate, and water hydrogen bonding near the interface are likely necessary conditions for nanobubble stability. We concluded that gas nanobubble stability does not necessarily require three-phase pinning sites.