Disappearing Workstations

I have a network of about 23 IBM's >(not domain)< The
school that I work in is a little SLOW in needed funding
for a sufficient server. Every now and then one of the
stations disappears out of nowhere. Might come back after
checking on it after some time, might not. At times I have
to undo file and printer sharing and enable them again for
the station to be seen again.

What I have been taught is, a network should have no
more than 10 stations within it. But what I didn't learn
is what is the primary reason behind that best practices
method. Is it strickly because it would be too taxing on
an administrator or because you would experience wierd
stuff such as what I'm going thru presently.

Can a peer2peer setup handle that many more than 10 within
the same group w/o problems or no??

If anyone can clarify this unknown for me I would
appreciate it very much.
THANX N ADVANCE The Rookie Wayne B.