I've worked with a few online programs that present students with drills / exercises / etc. for a period of time before deciding that they've 'done enough' for the day (e.g. Reflex Math). How do these sites (or their implementors) decide what's 'enough'? Is there research that says that children will only be able to retain a specific number of new facts in a period of time?
Many of these sites use a model called the Spaced Repetition Model. In particular, I'm most familiar with how Duolingo used to do it a few years ago, as I worked there. Khan Academy seems to do this as well. In principle, though, the idea is the same.
As a high level explanation, these site group together types of questions (e.g. for language each word is a type of question, for basic addition "one-digit addition" might be a type of question. As it gives you questions, everything starts out equally likely. As you answer questions correctly, it "schedules" them to be given further and further in the future (usually on an exponential model). Eventually, it asks you these things so rarely that students don't feel like they're getting things they already know.
Other sites (though, it seems increasingly rarely) use a "mastery model". Khan Academy used to do this, but I believe they've all-but phased it out. The idea here is if you get a type of question correct $n$ times in a row (where $n$ varies on the implementation), then it never asks it to you again.
Another article explaining Khan Academy's approach is here: http://david-hu.com/2011/11/02/how-khan-academy-is-using-machine-learning-to-assess-student-mastery.html