oil disappearing from pan

Simply put, your oil isn't hot enough. If you add vegetables to cold oil in a cold pan and then heat everything up, your veggies (or just about anything else) will soak up the oil. Heat the oil in the pan until it starts to shimmer and a drop of water sizzles, dances and disappears. THEN add your veggies. The very definition of "saute" comes from "to jump and to dance". It's all about the hot oil. Be wary of your oil's smoke point, don't let it burn, but get it good and hot.

EDIT: A friend in chat dug up this video. I like that it shows using water to test the heat of the oil. If you're trying to brown slices of eggplant, the way she treats shrimp is very similar to how you want to handle eggplant slices. Stir-frying is a different technique, but the hot-oil rule remains the same. Saute Video

This may not be the root of your particular problem, but you may be losing a significant portion of your oil due to splatter and aerosolization. If your pan splatters a lot when you initially add your vegetables, this may be part of the problem. To limit splatter, make sure the vegetables are completely dry before putting them in the oil. At a minimum, dab them with a paper towel. You can also lightly salt the cut vegetables and place them in a colander for 5 to 10 minutes before cooking and then squeeze out and/or soak up the moisture using a paper towel. This is a very common technique used for eggplant. Finally, you may be using more oil than you need. Experiment with using less oil initially, and adding more as necessary as the vegetables start to heat up.