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So my question is, is it natural for pianists to feel a certain amount of pain after practicing demanding repertoire, and are there times when you ignore the pain, and if so, how do you know when to ignore pain and when to take it seriously?
No, pain is not natural. Further, I do not think that a pianist performing anything within their technical capabilities will have pain. There are great histories of series of the most demanding performances within a single night (like 3 concertos) or week (5 demanding recitals), etc. For a pianist to perform is like having a cheetah run at 70 mph or a fish swim at top speed: that's is what it does.
Fatigue is another matter and is certainly to be expected. To be sure, one can approach playing with the "wrong" technique, and their is some variation of anatomy to be considered, even within a single pianist. I for example, have a
much shorter tendon (extensor digitorum communis, see at
http://www.bartleby.com/107/illus424.html) connecting my LH 5th finger to my 4th finger, which causes a severe restriction of extension (lifting) of that finger when the 4th is down and not able to give it more freedom. It hurts when I try to mirror what my RH can do. Plus I would have to add this: pianists are not immune to disease

. There are disease states that affect the hands, like Rheumatoid Arthritis, Osteoarthritis and Scelroderma, (Carpal Tunnel Syndrome is not a significant pathology in pianists to my experience) that may also be a consideration. In summary, it should not hurt a pianist to practice and perform any more that it does a bird to fly! With one exception: in the early stages of developing a particular technical aspect when one may be using muscles/tendons not used before or in a manner not used before (no different than the Weekend-Warrior, or first leaf-raking of autumn, first snow-shoveling of winter, or spring-cleaning, etc.), one can certainly develop an expected soreness that usually achieves its zenith at 2-3 days afterwords. Another exception, I believe would be the finger tips. If a repertoire or practice regimen has an unusual amount of percussive FF-FFF playing, it would not be any more unusual to expect soreness of the finger tips, than it would to expect a ballerina's toes to hurt from "too much"
en pointe. In either case, nothing that a little rest and recovery time wouldn't fix.