The answer to your question is yes but it is small. A small amount of H₂O breaks down when attacked by UV radiation... some of the oxygen recombines as ozone which is gravitationally bound to earth. However diatomic hydrogen does in fact achieve escape velocity and leaves the earth. So while strictly speaking water does not escape, hydrogen does. A place to read about this is in the book moons and planets by W. Hartmann or any other decent planetary science books.

Some astronomy books have decent sections on planets; others are too deep sky oriented and don't discuss planetary atmospheres very much.

Yes, water does escape into space -- there are several mechanisms, but the most common one is breakup of water via ultra violet radiation, which frees a hydrogen atom. This atom is not gravitationally bound to the earth as hydrogen is so light that typical thermal energies can exceed escape velocity relatively easily. As for how much, that is a really good question, and one I don't know off hand.

However, the people who do climate modeling need to be able to model various gas concentrations and water vapor is very important, so they must have some sort of estimates. -- A good source would be writing (or email) to the U.S. Geological Survey -- their Web site is:
click here -- also look at
click here, too

Sorry I can't estimate the loss rate for you -- but I am sure these people can do it.

Water vapor, e.g., the atmosphere, is "held against" the earth by the earth's gravity. There may be a trace amount of the atmosphere escaping over time, but it would not be a significant amount. In order for a significant amount of water vapor to escape, it would need to achieve escape velocity (the same as a rocket) to leave the earth's atmosphere.

My Resident Science Expert tells me that the water loss should be very small, because of gravity. Hydrogen and helium are escaping because they are light and can reach escape velocity - molecules have some amount of kT worth of energy (maybe 3/2 kT at room temperature), which gives them a kinetic energy of 1/2 m v².

Since m, the mass, is so small for hydrogen and helium, the velocity is large. But for things like nitrogen, oxygen, and water, m is larger and v is smaller and so very few molecules will reach escape velocity in the upper atmosphere.