General aviation instructor pilot reported flying below circling minimums in visual conditions on a practice circling approach with a student. The instructor prompted the student to regain altitude during the practice circling approach.

Narrative

I was practicing a circling approach with an Instrument student and when circling; we descended a bit low. I advised my student we needed to get above the circling minimums for that approach and upon adding power; the airplane did not climb very fast. My student also ended up taking out flaps which then let us sink low while we were in the left downwind for 35 at TVY. In the downwind; we were in the range of 4700-4800 indicated and could not seem to get our altitude back. We ended up making our base turn and the aircraft continued to sink low in our base turn at which we then added full power to gain some altitude. Although we were both paying attention; for practice circling approaches; it is important that we pay attention to our altitude. The minimum altitude on circling approaches is not to be broken and with days that have high Density Altitude; it is important we take that into consideration. For future circling approaches; I plan to not allow my students to get too close to the minimums for circling approaches so we don't allow ourselves to get too low. A better briefing of how the circling approach should go will also help the end result in the future..