Instructor Pilot reported a loss of power in a Cessna 172 during cruise flight and performed an off airport landing.

Narrative

Pre-flight/Engine start normal. Engine run-up everything normalTakeoff Runway XX with a right turnout to the south following air-tractor in the pattern. The climb check completed during the transition climb from the runway environment to climb phase of flight. Utilizing Foreflight I put in a direct course from ZZZ to ZZZ1. The top of climb reached approximately 10 miles south of the airport at 5;500 feet. I trimmed for straight and level flight ran cruise checklist (leaned mixture; set cruise throttle 2400 rpm; landing lights off). Shortly after cruise checklist compete (roughly 5 minutes) I remembered C172H model quirk above 5;000 feet and switched to single tank (left). Not long after this (at this point I do not recall the time sequence of events) the engine sputtered. This was not uncommon for this to happen in these airplanes occasionally so I checked fuel selector and re-leaned the mixture in case I had the setting to lean. The engine smoothed out for a second then sputtered again; this time to a greatly reduced power setting. This time it was more alarming. I pushed the mixture in (full rich) and set the fuel selector to both; nothing changed. I applied full throttle and the engine came back a little for about 2-5 seconds and died off again. Still trouble shooting I referenced the checklist and saw nothing to be done as the engine was still running but not have any power. Once I reached about 3;000 feet I knew I did not have much time let so I started to circle a place to land and [requested priority handling] on 121.5 giving all information I could. I could still push the throttle out then in and gain a short boost of power but that was it. I knew I was going down and boosting the power a little was just going to put me out of reach of my landing location so I gave that up and prepared to land. I did not shut down per the checklist because I knew I had time and still wanted my radios and flaps available and the field ahead was an easy target. I executed a soft field landing with full flaps and came to a complete stop gently in a pasture. I then reported down and safe to a nearby pilot who was in contact with ATC. I noticed the engine was still running and I could bring it up to about 1500 rpms. I then shut down the airplane to exit and investigate the issue. After a quick post flight and oil check I could not determine the cause of the power loss. After talking with a nearby farmer I decided to better position the airplane in the field. The airplane started right up and seemed to have full power again so I position the airplane a little better in the field trough soft field taxi and secured the aircraft as best I could through applying parking brakes and control locks.Through further research I believe the aircraft could have experienced vapor lock in the engine. This could have been exacerbated by my use of the checklist in this situation. This theory is not confirmed and mechanic will be notified and any findings will be noted before the aircraft is returned to service.