C-172 Flight instructor reported a loss of AHRS in IMC during descent. Instructor received ATC assistance to continue to destination airport.

Narrative

The aircraft involved is a new (<1 year old) Cessna 172 with the G1000 NXi (Nav III) avionics suite. I squawked this particular aircraft the previous time I had flown it; approximately three days prior; for an in-flight AHRS failure. In the previous incident; another student and I were departing VFR from a satellite airfield having done a stop-n-go. As we were climbing out of the airport vicinity; I glanced at the PFD (Primary Flight Display) to ascertain his speed and noticed the attitude showed us in a right bank of about 10º. It had been turbulent all day so that would not have been completely unusual; but because I hadn't felt the bank; I looked up to observe the natural horizon and realized the PFD attitude indicator was not correctly displaying attitude information. It quickly went black and flashed red Xs before an AHRS Align message displayed. Another instructor advised me that she had experienced this once before and that a third had as well. The maintenance entry returning the aircraft to service stated connections had been cleaned and checked but the issue could not be replicated. On the day of this reported incident; I was on an IFR flight plan with a student proceeding from ZZZ1 direct to ZZZ; initially at 5;000 MSL. We were in and out of clouds throughout the flight; probably 70-80% of the flight was without either contact with the ground or a discernible horizon. At about 15 miles from ZZZ; we were given descent instructions and began to comply. At approximately 4;500 MSL; I noticed a turn on the HSI (Horizontal Situation Indicator) that didn't match up with our attitude information. I looked at the standby attitude indicator; a Garmin GI-275; and also did not match our PFD's attitude information. I directed my student to use the supporting turn indications to break the tie and help keep the wings level until we descended into VMC. I advised ZZZ Approach (XXX.X) that we were experiencing AHRS failure; had a backup; and would like to avoid continued flight in IMC once we exited. This time; the AHRS never seemed to reset itself; i.e. the screen never blanked; put up red Xs; or otherwise warned us of failure. We also reported that we needed no emergency assistance at that time and that we would continue the flight in VMC. We broke out of the clouds at about 3;500-4;000 MSL and continued the flight. We were queried about our intentions to remain on the IFR flight plan or to return to ZZZ1 on VFR Flight Following. I initially said that we could do 'whatever is easiest for you' as I was confident that we could maintain basic VFR on the return trip. We were directed to ZZZ; about 10 miles ahead. My student called the airport in sight but ATC caught that we had instead spotted ZZZ2. We reset our expectations and continued onto ZZZ for a touch-n-go. During the return flight; we were handed off to one of the satellite sectors (can't remember if it was XXX.Y or XXX.XX). As we continued northwest-bound; we were asked to climb to 4;000 for traffic. I reminded the new controller that we had previously experienced an AHRS failure and that I would not be willing to re-enter IMC. At this point; we were in level cruise flight at 3;000 MSL with a cloud layer very nearly above us. A climb would have put us back into the clouds. He then gave me a vector to the north and around the traffic. We cancelled IFR as soon as we had the field in sight and squawked the airplane again. I think we handled the initial problem well enough. Finding conflicting information; we sought other information to complete the picture; break the tie. A lot of EFIS (Electronic Flight Instrument System) failure training is focused on various elements showing a red X when a component becomes unreliable. That did not happen on this occasion. I was able to record a video showing both attitude indicators with a 5º difference in bank.When queried by ATC about our intentions; I initially told her that we could remain on our IFR flight plan or switch to flight following; whatever was easiest for them. Looking back; I am glad we were kept on the IFR flight plan and I wish I had said as much initially. There are several towers and other obstacles near ZZZ2 that were not very far below us. To maintain basic VFR; we would have had to descend and would have been closer to these obstacles. I understand that we did not declare an emergency; but we were in a precarious situation. When we got handed off to the second controller on our return leg; he asked us to climb for traffic; which would have put us back in the clouds. He didn't give us any difficulty when I refused his instructions and explained why. I think either I could have called a PAN-PAN or perhaps there is an opportunity for this type of situation to get explained when an aircraft is handed off to the next controller. I've been to the ZZZ TRACON and know that these two frequencies are on different walls; so the second controller would not have been fully aware of the issue as it developed.