I just fixed my furnace and it kept turning off and on as well. I have never seen this suggested online yet and had to find this out myself. it turned out the tube that the condensation water comes out of was frozen and blocked all the way back in the system. I had to open up the release valve near where the hose connects to the furnace to let out the backed up water and it worked perfectly after. Currently working on thawing out the ice in the tube and then I'm going to add a insulation sleeve to it to avoid this situation in the future.
I found this as well.
the release valve is called a zone valve... might need to replace it, they go bad sometimes. i work on a lot of boilers, if you are handy enough id change em out... all you need is the valve and a torch and flux and solder.. if you got a little wiggle room on the pipe to connect it... if not cut a couple more inches off the pipe and add a coupling and some more pipe.. then put flux on the fitting and zone valve and pop the zone valve in and solder it all together... if its only frozen, look for leaks, if you got none and the zone stays open youre good to go. if the zone keeps shutting off pop a new valve in.
you need this..
http://www.supplyhouse.com/Taco-571-2-3-4-571-Sweat-Zone-Valve?gclid=CLfQ_4TfqssCFdGQHwod_WsLPw
its a little pricey, but if you can do it yourself youre good to go.. if not.. a plumber is going to rock you.
being residential im guessing its 3/4" .. but ya never know, if you order make sure you order it the size right.. its the size of the copper its on... if you call someone out id order the shit anyway.. plumbers mark up material and labor is pretty pricy, if you called me out that valve would be about 150 and then 95 an hour labor, and im extremely cheap for a licensed/insured plumber.. hope this helps.. also if you do pick up the zone valves.. go with Taco (pronounced tacko).. dont get some shitty knockoff thatll break a few months later