Syslinux - Mar 2007 - TFTP server gets stuck for me. But not all of the time?

I finally got around to trying to learn how to setup and configure a
PXE server on a spare system I've been using as a router/download
server.  It took me forever, but I finally got everything more or less
together and in a working form.  But it seems I'm having an unusual
problem outside of all this.

I never really got a TFTP server fully working.  After several failed
attempts on various different servers (including distro packages) I
managed to get tftp-hpa to compile and work sucessfully and it seems
to be running just fine.  In fact, on occasion when I booted pxelinux,
it worked sucessfully, loading up the full menu, background graphics,
and all and it even booted sucessfully from there.  However, since
then, nearly every single time I've tried it just kind of freezes.  It
loads the DHCP portion just fine, but when it tries to get the data
from TFTP it just gets stuck and times out with the message "PXE-E32:
TFTP open timeout" and the second try never even times out.  I even
tried running a TFTP client on the sever locally and it just kind of
got stuck there as well, though I found a zero byte file where it
would have downloaded, so I guess it doesn't get anything at all when
it tries.  So far the freezing has been pretty inconsistant, lasting
most of the day once it starts, but often working without a problem
for whole hours at a time, so I haven't really been able to figure out
exactly what could be causing it if it were some outside thing at
fault.