In general the z-sensor circuit is not working properly when you have one of the following issues:

• Z-axis only moves a few mm downwards when homing.
• Printing/extruding in the air.
• Bed leveling not working. (G32/G33 leveling failed)
• Persistent "Z-sensor triggered" message when idle (only for Pro-series)
• During printing, the z-axis only moves downwards (TEC/3.x series)

In general the following things need to be checked.

• Connection to the mainboard. Inspect if wires are properly mounted and no loose metal strands.
• Wiring. Wiggle cable during homing when placing bed completely. If it stops somewhere halfway, most likely the cables are broken somewere
• Sensor itself. Exchange the sensor with another one (from for instance the x-axis) and check if the other sensor works. 

Other specific cases to check are described below

Tec specific
The z-sensor for the TEC is an inductive sensor. The indication light must burn when the sensor is further away from the bed than 4mm.

Known cases with the inductive sensor and when doing an upgrade from 3.0 to tec 4

• Not enough voltage supplied from opto-sensor port. Older revisions of the FELIX 3.x mainboards provide a lower voltage. So in case of an upgrade, to make the sensor work, the 12V from the powersupply itself should be taken.
• Forgot to place the flexplate on top of the bed.
• The sensor is mounted too low. So when the nozzle is touching the bed, the clearance between the sensor and the bed is too small. Move the sensor upwards 1mm. Also reset the eeprom after doing this. Then do the calibration runs again.
• Starting conditions are too far off. If in some cases the levelness of the bed is too far off, the printer cannot find a solution. In this case try to adjust the levelerwheels and help it manually along so it is closer to the best leveling.
• Sometimes the calibration is completely messed up and it is then advised to do a eeprom reset, to start with a clean slate.

Pro series specific
The pro-series has a z-sensor contact in every hot-end. Correct workings of this sensor is extremely important for all the automated features to work properly.

Most obvious way to see if something is wrong, is the z-sensor triggered message when the printer is idle. This means that one of the hot-ends are pushed upwards from its contact. When you start a print, this should clear itself. If this does not, then further troubleshooting is required.

Please read the following guide for more information.
HOW TO FIX Z-sensor triggered.