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I think it is possible that the paper pickup rollers have become slick with age and are not making firm enough contact with the paper, in consequence, to propel it into the printer.
If the problem might possibly be owing to aging roller surfaces (for paper is fed into faxes and printers with rubber or plastic cylindrical rollers, that propel the sheet into or through the machine)... then you should try cleaning the rollers in the problem area where feeding is not happening.
Remove all paper from the machine, unplug it, and open it so as to have access to the rollers in the problem area where feeding is not being done properly.
Take a clean high-quality lint-free rag cloth, moisten it with rubbing alcohol, and rub the rollers firmly all over their paper-contacting surfaces, three times over.
(If the rollers are hard to reach, there is another way to clean them... let me know if that is the case, and I will detail how to do the cleaning.)
Allow 5+ minutes for drying-off, then reload the paper, close up the machine where you opened it up, and then try again.