My winchester furnace shuts down mid cycle and we have to turn it off and back on what can cause this?

First do you have an evaporator coil (a/c coil) on the furnace? Second, have you tried to bypass the thermostat? Does the furnace restart itself after a short while or go completely out? Is it an 80% furnace (does it have a metal flue)? There are three principle concerns at this point: 1) restricted air flow (dirty a-coil) 2) a bad fan/limit control or 3) bad thermostat. Let me know and we can figure it out from there on.