We're going off topic here a little, but I've seen a Metrel EasiTest give incorrect readings on continuity due to a very unusual problem. The problem was that the switch for the 'Start' button had become high in resistance - it is the most used switch after all. Each switch has a different value of resistor in series with it, the microcontroller 'knows' which button you've pressed because it receives a different voltage. The varying resistance of the Start switch caused it to occasionally 'mimic' the 'Cal' switch (Metrel's term for continuity zeroing). Since this was happening with the leads connected to the installation circuits being tested, rather than being shorted together, when the tester did produce a reading it was lower than expected and not consistent due to 'phantom re-zeroing' happening occasionally. A new Start switch cured the problem.
Thinking again about the OP's problem, this is a Fluke 1652C and therefore should have the latest type of test leads with thick black rubber insulation. These are much better quality than the coloured leads supplied with early testers. If the probes are removed, just one lead at a time can be connected to the tester's L (V Ohms) and PE (COM) terminals, forming a loop. Thus the leads can be checked individually for high resistance/breaks/zeroing issues. It is unlikely that all 3 would be faulty so if none seem to be stable this would suggest a problem with the tester itself. A poor connection on the fuseholder in the battery compartment could produce similar problems.