Team,
I have a customer using BQ24040 in their latest design. In every case that they've attempted to charge their system, although the current seems to start at about the right value, it steadily drops over 4 hours until hitting constant voltage mode.
They also have a different 5 V 1 A supply that they tested, which never even got close to the 1 A charge current (the Glob 1 A in the workbook). I would make a guess that this is more related to the supply than the charger, but thought I'd include this in case it provides any insight.
I have attached the results from their testing.