Machine never raises Z axis to probe while leveling the bed (no replies)

I have a problem with my recently added inductive probe and Marlin 1.1.9. The probe is connected to the Z min endstop, and works fine for homing. The printer moves in XY to the middle of the bed, raises Z, lowers Z until the probe senses the bed, raises Z again and lowers Z more slowly. So far so good.

I confingured AUTO_BED_LEVELING_BILINEAR, and when I run G29 after homing, the following happens:
The printer lifts Z, moves in XY to the first probing point, lowers Z until the probe senses, but only once. It the moves in XY to the next probe point, but it never lifts Z again. Instead, it quickly drags along in XY to all other probe points, and gives identical numbers for each point.

I tried deliberately skewing the bed, so that it leaves the initial Z height that gets probed on the first point. I notice that when the LED on the sensor goes off, the Z steppers move down a little until the LED is on again, and then the machine continues through the remaining positions without ever moving Z again. The result is that I get two different numbers: one for the first to Y rows, and one for the last two Y rows.
Why does the machine never lifts the Z axis again?

Here's my config: [gist.github.com]