Welcome, Unicorn!
First off, do remember that a child in the tested range you report is still a bright and very capable learner, who will likely need more than the typical classroom provides, even if not nominally in the (arbitrary) gifted range. In any case, one IQ score does not make a more valuable individual than another score.
Secondly, yes, fatigue can affect performance on just about anything, including formal cognitive assessments. Typically, it affects memory and speed tasks the most, but any kind of task could be affected. Many other factors affect test performance as well, including age, anxiety, experience, attention, medication side effects, allergies, etc.
My general position on testing is that it should only be undertaken with a specific purpose, usually for 1) access to resources, or 2) elucidation of and intervention planning for learning challenges. Families will, of course, make their decisions based on their specific culture and needs.
