This type of problem with older computers is to be expected and most of the time they are simple fixes such as drive cleaning, bad disks and such. Occasionally it is a bit more, but even then its not too big a deal, and usually fun to open up and fix things.
I just had this happen on my Atari 1040 STf and wrote it up to share the ordeal here: http://fetchrex.com/2017/02/12/oh-no-atari-1040-st-floppy-drive-issues/
I have a good sized collection of classic computers from 80s like an Amiga, Mac Classic, Nextstation, etc. and the Atari ST is no different in the types of care and feeding they need... makes me love them even more after their tune ups. :-)
Russ