I get this a lot with my BL Touch. Its always been been the connectors (I use latched Dupont connectors at the hot end side). You could just cut off the connectors and solder a wire all the way back to the duet to eliminate them. What I found worked very well was a 3 x 2 standard block Dupont Connector (not latched) that I used to connect the 3 logic pins to the 50Pin Male connector on the Duet Wifi board (Orange Brown and yellow). It will be these three pins that will be causing the problem.
If you have used the connectors at the hot end side ... the cable they provide is very thin (shit actually) and hard to crimp reliably. I soldered and heat shrinked some solid core wire and used that wire to crimp pins for the connector. It mostly fixed my issue.
FYI Continuity testing dose not always pick up the issue if is a broken pin barb on the connector it can get pushed back in the housing if that's broken and you don't spot that when you continuity test further up the pin on the exposed bit where the barb latches. What happens is that when connecting male to female the broken pin gets pushed back and makes a very poor contact.
Good luck this drives me nuts too.