And again....
May be you can explain the different statistics every time 
First, make sure you're using SI7 or SI8 for 6.5 digit meters. I usually use SI8 on mine. Keep this consistent between meters of the same digits.
Second, make sure you have a lot of warmup time for both the meter and the reference.
Third, flatline usually means the meter is no longer reporting. You will need to restart the test. I usually use the save to menu function in TC, then restart TC and run the script.
Beyond that, you will need to include more meters to understand what is happening. For my reference, I've used the same reference for 8 or 9 bench meters, with up to 5 or 6 connected at 1 time. This gives me a solid baseline to know what the best results might be.
I start with 2-minute tests, and let them run longer. Each test number is the same test sequence (Test 1- 2 minutes, 5 minutes, 30 minutes; Test 2- 2 minutes, 5 minutes, 30 minutes; etc. - I just take new screenshots at each test time).
If you're using a single ref with a single meter, it's hard to know where the inconsistency is. It helps if you can use a calibrated voltage standard.
It would also help if you're able to monitor ambient temperature. Temperature change is the most common reason (besides a broken device) to see instability in your measurements.
Thanks,
Josh