Hmm... this problem sound awfully familiar. I'm sure just about
everyone here has come across this situation at least once.

Unless the faceplace rusted on the spindle, or someone came into your
shop in the middle of the night and welded it on, it sounds like it
'simply' got too tight on the spindle. A couple of vise-grips or
simular gripping devises are in order. There might (should) be a big
nut on the extreme end of the spindle (twords the headstock). use one
vise-grip onto this nut, and use the other visegrip somewhere on the
faceplate. If the taper of the faceplace is flat, then grip there.
Then turn each vise in the opposite direction. A hammer might be
needed as well to get it started. DO NOT secure the visegrip on the
threads of the spindle, as this will only ruin them (lesson well
learned for me). Maybe some WD-40 or other liquid lubricant will aid
in the attempt. See if there is a spindle lock somewhere on the lathe,
ad this will make your job much easier.

If and when you do get the faceplace off, check the threads on the
spindle and the corresponding faceplate. Some dirt or other object got
lodged in them. If they are worn in some spots you might consider
replacement.

As far as preventing such in the future, I take the same aproach to
auto mechanics. Everything doesn't need to be tightened down with the
strength of King Kong, especially in this case. Typically, just hand
tightening the faceplace untill it won't go anymore with light pressure
is sufficient.