When the temps drops below set temp on thermostat it won't automaticlly come back on unless I manually shut the system off and turn it back on. Is my thermostat wired wrong?

If the fan is not kicking in it is going to do that. Try turning the fan to on at t-stat and see if furnace stays going. If so it can be limit switch/camstat if you don't have meeter just call a pro. You have to trace the voltage down and find the problem.

It really helps if we can get a make and model #. The old and the new differ a lot. A long with the thermostats being used. All the info you can give will help.