That sounds like condensation building up (water) until it gets hot enough or hits the right condition to "boil" it off. I believe this is fairly common in cars where shorter trips are the norm.
What happens is condensation builds up and replaces oil as it's "used up" or drips. That's what makes it APPEAR to keep a steady level reading. Then, when the conditions get right, water (floating on the surface of the oil in the oilpan) flashes off and gives that sudden drop in reading.