Chris,
You've given me something to think about.
I just used five canvases trying to get this last portrait right. I felt it was a shame to throw them away. But you are right, canvas is fairly inexpensive. I do understand and appreciate the importance of perfect practice. However, the reason I asked this question was to find out if a painting will last if it's been done on a canvas which is previously painted on. If there were no serious problems with doing it, why
not do it?
Michele, it would indeed be a shame to have a really good painting on a crummy canvas! However, if a re-painted canvas is not necessarily crummy, then wouldn't it be okay to have a masterpiece on a repainted canvas? I will bear in mind the fat over lean rule.
I appreciate Michele and Chris, your suggestions and experience. Thank you very much!
Richard, nothing I have is years old...yet.

Thanks for sharing what you've heard about this matter.
I have heard here two reasons that it could be bad to repaint a canvas. a) paint becomes transparent over time, b) the hastles of painting fat from the start and not being able to do an underpainting decently.
Those are two very good cautions and I will keep them in mind.
I come from the "throw away" generation, but I attempt to be more conscientious. Sometimes it's a good idea, sometimes not.
Alexandra, you said that gesso could peal off if put over oil paint. Is this true even of oil-based gesso? I can use your method and just mix up some neutral oil paint and spread it on the canvas.