Why does my carved design disappear when I glaze it?

Your teacher was talking about exactly the right thing. Glossy glazes are runny in the kiln, and when they melt they flow into the low spots of your carving, which fills the grooves up like water settling in a puddle. On a dark glaze that means your nice deep lines fill level with the surface and disappear. It's not that you carved badly, it's that the glaze undid the carving at the high temperatures.

I had something similar happen with a leaf pattern I pressed into a bowl, so I feel this. Someone at my studio suggested brushing a lighter coloured glaze into the lines first and wiping the top with a sponge, so the design shows up as contrast instead of relying on shadow. apparantly that's a common trick. My question is, does that work on the rounded parts too, or does the sponge wipe the lines clean out on a curved surface? I tried it once and couldn't tell if I was wiping too hard or if it just doesn't work on curves.

I think the clay body itself might be playing a bigger role than the carving depth. Sometimes the porosity of the clay pulls the glaze in too aggressively before the kiln even starts. When I work, I always ensure the greenware is stable by holding my bisque firing at 1000 degrees for 45 minutes. This helps lock down the surface so the glaze behaves more predictably. If the clay is absorbing too much moisture or has high permeability, the glaze will run deep into every texture regardless of how much you scored it. Consider running a simple absorption test on your finished piece.

I think the contrast method mentioned is prolly the easiest way to solve this specific issue with dark glazes. I had tried that exact technique when working on a textured plate, and I found that just brushing the lighter color on was not enough to get it deep enough into the grooves. My trick was to mix the chosen glaze with extra water to make it really runny, almost like a slip. This helped the color wick into the carved lines before it could dry, keeping the detail much sharper.

Update: I tried using the light colored glaze in the grooves first, and that defintely helped make the design pop more on the surface. I still have trouble with the clay body seeming to pull the glaze in too quickly, though. Does anyone have advice for reducing the porosity of the clay before I start glazing?