I have been doing more reading on osteoporosis. There is nothing anywhere I have seen yet that indicates sweating being a cause. There is quite a bit indicating that a diet that is too high in protein causes a negative mineral balance in the body, with calcium being one of those minerals. Tests have shown conclusively in thousands of cases that intake of protein above certain safe levels caused a negative mineral balance with increased amounts of calcium let out in the urin. The more protein the subjects took in, the more calcium they flushed out in their urin. Heavy cigarette smoking and ingestion of alcohol are also noted as causative and or contributing factors. Two authoritative sources say DO NOT take calcium supplements like pills and tablets. They also say it is not necessary to take supplements of vitamin D, and vitamin D supplements can be harmful.
If you want the sources of this information and page numbers, I can give them to you. There is quite a bit more. The original question was a medical one, and not related to cycling per se. The point is, if you are losing a lot of calcium through sweating or through the urinary tract, pumping pedals and sweating are not the causes of your osteoporosis. A negative mineral balance has other causes.
Large scale, extensive medical studies were carried out in Africa among the Bantus and other tribes known to have a diet low in meat and protein and high in fruits, grains, and vegetables. According to this study doctors were unable to find even one single case of decalcification or osteoporosis. Vitamin D is stored in the liver and generated when solar radiation comes into contact with your skin. Even if you were to get no sunlight at all for long periods, it might take several months or even years for the vitamin D in your body to become depleted. Too much vitamin D can contribute heavily to osteoporosis; it can be harmful, and even cause death. You need it, but only in limited quantities. The same with protein. It is very useful in absorbing and assimilating calcium, but too much causes a negative mineral balance, and you lose calcium. That's all I have time for right now. What it all boils down to is what our parents, and grandparents, and their parents before them preached. Eat fresh fruits, fresh vegetables, whole grains and whole cereals.
Avoid processed foods and hightly refined carbohydrates as much as possible. If you eat them habitually over a long period, you are treading a sure path to problems with your health.
I have paraphrased this information from a book.
Pritikin, Nathan.1979. The Pritikin Program For Diet and Exercise. Grosset and Dunlap.27,53,375,398,379.
There is more.