The brief
The 730Li was leaving fresh oil drips on the floor, and they were landing right under the join between the engine and the gearbox. The dipstick was dropping faster than a healthy engine should lose oil, and the cabin would catch a burning smell after a run on the motorway.
The spot the oil drips from is the clue. That area only weeps when the seal right at the back of the crankshaft, behind the driveplate, has given up. It is a small rubber seal doing a hard job, spinning against the crank all day, and when it hardens with age it stops holding oil in. The burning smell is that oil reaching the hot exhaust nearby and cooking off.
The diagnosis
On the lift the source was confirmed: oil weeping from where the crankshaft passes out of the back of the engine, then tracking down the bellhousing and dripping off the bottom. On this engine that can only be the rear main seal.
The catch is the access. To get to that seal the gearbox has to come away from the engine and the driveplate has to come off, which is a big job, not a quick reseal. The owner saw how fast the oil was disappearing and gave the go-ahead, because the alternative is topping up forever and watching the level.
The work
The gearbox fluid was drained, the drive shafts and propshaft disconnected, and the gearbox supported on a transmission jack and drawn back off the engine. The driveplate came off to expose the rear main seal.
A new BMW-spec rear main seal went in, and while everything was apart the gearbox-side seal was renewed too rather than leave an old one next to a new one. The driveplate was refitted to torque, the gearbox mated back to the engine with fresh bellhousing bolts, and the box refilled with the correct ATF.
The outcome
Dry bellhousing, no drip on the floor after a long road test, and the oil level holding where it should.
The 730Li went home with the leak fixed at the source. For the owner that is the end of topping up and the end of that burning smell on the highway. And because this seal does not get disturbed again unless the gearbox comes out for something else, doing it properly once usually means it stays fixed for the rest of the car's life.