Hydrogen and Oxygen do not separate in water because the energy of a water molecule H₂O is less than the energy of separate H and O atoms. Nature always like to go to the minimum energy state; nature can be LAZY!!!

The water molecule (H₂O) is held together by covalent bonds. A covalent bond is formed when two atoms share a pair of electrons between them. Covalent bonds are lower in energy than the corresponding separated atoms. This is because when two atoms come close to each other, the atomic orbitals of the atoms overlap and mix to form molecular orbitals. Two atom orbitals which overlap will mix to make two molecular orbitals (one with lower energy than the isolated atomic orbitals (bonding) and one with higher energy than the isolated atomic orbitals (antibonding)). If each atom contributes one electron to the bond, then the electrons can spin pair (one is spin up and the other is spin down) and move to the lower energy state that is the spin-paired bonding molecular orbital. Since covalent bonds are lower in energy than the corresponding separated atoms, the atoms stay bonded together rather than separating. Brenden, Materials

In water, hydrogen and oxygen are held together by chemical bonds. These bonds are strong, so in most of the conditions we encounter, hydrogen and oxygen don't separate. However, these bonds are not impossible to break. In fact, if you apply electricity of a proper current and voltage, you will split water to form hydrogen gas and oxygen gas!

Hydrogen in water is chemically bonded to oxygen. It takes energy to get them to separate, just as it releases energy (in the form of heat) to unite them.