The ADR03 may not be sufficient to supply the required AIdd to the System Monitor.
Looking at figure 21 of the ADR data sheet (page 12):
You can see that once the load current gets close to 10 mA at 25C the drop-out goes above 2V.
The 125C graph goes above 2V after about 5.5 mA.
Therefore, there is a temperature dependency on the exact value of the reference.
Therefore, the ADR03 was removed from UG192. The other two references mentioned in the User Guide are the REF3025 and MAX6043.