How many times can you sharpen most lawn mower blades before you have to throw them away?

Blades that are not damaged can be sharpened several times. If they get nicked or bent than they should be replaced. It is much easier to remove the blade from the mower to sharpen it. Taking it to a shop might be easier but also more expensive and for the most part unnecessary. As far as how quickly they dull is tough to answer. If you are mowing an average lawn without hitting a lot of things, once or twice a mowing season should be fine. If you have mole hills, rocks, sticks, etc you will dull the blades a lot faster. Running over a mole hill will dull the blade to some extent immediately depending on what type of soil is in the mole hill. Sharpening a mower blade is so easy and quick that I don't have a problem doing it a few times during the mowing season. Just part of routine maintenance. It could also be noted that not all blades are of the same quality. That will also determine the sharpening cycle.