ECU evap test not running, won't pass inspection

If your EVAP monitor is the only thing NOT complete or READY, then you are fine to go back for inspection. (at least in Jersey)- Every car that's 2001 and newer is allowed to have one monitor incomplete and still pass as long as there are no active codes and MIL is off but functions properly.

That said, if codes were cleared then just drive the car- EVAP can be difficult to complete. It can take weeks to run or might not run at all in low ambient temperatures.
From the manual:
EVAP MONITOR (KEY OFF TYPE)
(a) Preconditions
The monitor will not run unless:
– The fuel tank is less than 90% full.
– The altitude is less than 8,000 ft (2,450 m).
– The vehicle is stationary.
– The engine coolant temperature is 4.4 to 35°C
(40 to 95°F).
– The intake air temperature is 4.4 to 35°C (40 to
95°F).
– Vehicle was driven in an urban area (or on a
freeway) for 10 minutes or more.
(b) Monitor Conditions
(1) Turn the power switch OFF and wait for 6 hours.
HINT:
Do not start the engine until checking Readiness
Monitor status. If the engine is started, the step
described above must be repeated.
(c) Monitor Status
(1) Connect the intelligent tester to the DLC3.
(2) Turn the power switch ON (IG) and turn the
tester ON.
(3) Check the Readiness Monitor status displayed
on the tester.

Sounds simple enough and sometimes I have no problems at all.
For some year Toyotas you can have Techstream (or a similar "advanced" scantool) run a self test on the EVAP system that will complete that monitor.

 

As you can see sort of buried in those instructions, the actual EVAP monitor test doesn't run while you are driving. You have to do enough driving of the right kind to satisfy the preconditions, but then you also have to park and leave it alone. The EVAP monitor test runs around six hours after you park and turn the car off. (It is what's happening in the various "I went out in the garage late at night and why was my Prius humming?" threads around here.)

It won't always be exactly six hours; it can depend on how long the temperatures/pressures take to fall from driving to ambient.

 

If it is losing monitor status when powered off, you might check for a problem in the B+ circuit powering the ECM's memory during power off.

 

If your throttle body or injectors are very dirty you can notice hard starting if the ECM forgets its learned adjustments. If they're pretty much ok then you might not notice much. If it is forgetting after every drive, then it's never getting much chance to learn anything you would notice it forgetting.

A normally-functioning Prius ECM does not forget its monitor status between drives.

 

I would start with the wiring diagram (more info), find the circuit that supplies power to the ECM when the car is off, maybe find what fuse that circuit is on and look at that, then look at the voltage on that circuit at the ECM connector.

 

I am not sure of all the details of what is in volatile and what is in nonvolatile memory in the ECM.

I am only suggesting things you might check if you were right in post #4 that the monitor status is being forgotten between power-ons, which is not typical behavior.

 

Do you have access to Techstream? It's possible you could get more information using its readiness monitor utility (the one that lets you enter specific trouble codes and get the status back for their specific monitor tests).

I used that a lot while I was trying to get rid of the permanent P0102 I had for a year or so.