On some furnaces the limit switch breaks the primary to the transformer.
If that happens, you have no 24volts to the stat and it goes dead until
the limit closes again and the power to the stat is restored. (First
hand experience with mine last winter) The limit switch is there to cut
the burners off if the heat exchanger exceeds a certain temperature. The
most common cause of that is low air flow over the HE, and the most
common cause of low air flow is dirty filters. That would be the first
thing to check. There are a number of things that could also cause that,
inicluding a faulty limit switch. Of course, this limit switch thing is
only a semi edjeecated guess. If your filters are clean, you probably
need to have your system checked and serviced by a pro. On mine, the fan
portion of the fan/limit switch was bad and would not bring the blower
on at all, causing the limit to open after a couple of minutes. Good
luck Larry