C150 flight instructor reported rapid electrical failure; without early detection; resulted in return to safe landing at home airport.

Narrative

This was an instrument training flight focusing on VOR navigation. We were conducting a practice ILS XX approach at ZZZ; on the DME arc to intercept the localizer. Just prior to intercept; the student reported that she had lost the CDI needle; and the navigation radio showed a message of 'glideslope receiver has failed.' Within 1 minute; the transponder stated that it; too; had failed; and our GPS was flickering. At this point; I determined that we were losing electrical power. Since weather was clear; we were only 30 minutes from base; and familiar with the local area and route; I elected to return home. We were still on frequency with ZZZ Center and I attempted to transmit our intentions and situation; however; there was insufficient power to do so. Within another minute; we had lost all electrical power except for the intercom. I have the ZZZ Approach telephone # saved in my phone and attempted to call using Bluetooth on my headset. I was able to get a hold of a controller and attempted to provide an update with our intentions. Due to either poor connection; background noise; and/or failing equipment; I do not believe the full message was received.Our return to base was uneventful and we made a no-flap landing. Upon reaching the hangar; I called ZZZ Approach and let them know we were safely on the ground. The controller informed me that they were tracking us as a primary target and were going to have search and rescue check on us if I had not called.We are still troubleshooting the cause of the failure. The EIS (GI 275) as installed only displays system amperage on the main screen; preventing early identification of an issue. The student did check the amperage during the engine run up; but this was a meaningless number as it is not tied to the alternator. Post-incident testing showed this number would increase with an increased load on the system and manually taking the alternator offline via the master switch would not change it. The only other electrical data available is the battery voltage; but this is only accessible by navigating to a secondary page and would not indicate a problem prior to departure. Alerts are not prominently displayed and are indicated by a flashing white icon in the upper left section of the device. This is the same way the unit displays a message or non-critical alert (e.g. expired database). Since this icon is almost always flashing; it is frequently ignored (alert fatigue). I discussed with the aircraft owner about changing the parameters displayed to show alternator voltage or a charge/discharge state; which would readily indicate the health of the electrical system. On the incident flight we did not discover there was a problem until it was too late and everything began to shut down. I have started carrying my handheld radio even if I do not have my full flight bag with me. This would have let me contact ATC and would permit us to fly a VOR or ILS/LOC approach if we experienced the same issue in actual IMC.