The closed system does not vent to the atmosphere, so there should theoretically never be any loss of water. The only loss of water in this setup would be from a leak somewhere.
With an open system, the time between refills will largely depend on the relative humidity of the air around the system. Very dry winter air will suck more moisture out of the system, while hot humid summer air will not affect it very much.
Open systems can limit the loss of water through the use of "labyrinth" breather tubes -- long, thin tubes which make it difficult for water to evaporate away rapidly. Print cartridges often use breather tubes to allow air to seep in as ink is removed, but without the ink drying out quickly from exposure to the air.
If you use an open system, be sure to use either "soft water" or distilled water. If your home's tap water is "hard" and leaves a white or red residue on sinks and dishes, it will be bad for your water cooler. As the water slowly evaporates away it will leave behind these minerals which will eventually choke the water and radiator lines, and in the end lead to overheating and failure of your water cooling system.
Actually if you want to be safest, you'll use distilled water only in a water cooling system.
Even though "soft water" contains less minerals than "hard water", it still contains some and can still lead to eventual system failure. It'll just take a lot longer with soft water vs hard water.
Distilled water is commonly available in just about any supermarket, probably 50 cents per gallon, so it's not all that expensive.
Be sure to get "distilled" water and not merely "filtered", "reverse-osmosis", "sterilized", or "sparkling" water. Only distilled water has had all the minerals removed from it and so is best for a water-cooling system, whether for your computer or your car.
If it is properly closed and you make use of a additional coolant like WaterWetter once in 6 months will do... maybe even once in a year.
With normal water cleaning the system and pump every 2 months is the best.
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