Is it possible to quantify how often I should sharpen a whittling knife?
The need to hone depends on the variables:
- the knife (the steel, the edge profile, how well it was sharpened previously)
- the hardness or abrasive quality1 of the wood(s) being worked
- the total amount of use
- the nature of the use (any levering or chipping versus only draw-through cuts)
Is it possible to say a certain number of days/months/years, a certain number of minutes/hours of actual woodworking, an approximate number of strokes in the wood, certain number of projects or times per project, a table or multiplier by wood type for increasing or decreasing the sharpening frequency, or some other measuring guideline?
If you want to maintain the edge to a very high standard (which many whittlers consider an absolute must, for quality of work as well as safety) more frequently than you'd expect.
Even with some better knives some touchup work can be required periodically during a single whittling session because of how sharp whittling knives, in common with other carving tools, need to be maintained, and because wood is relatively wearing to steel (think cutting cardboard rather than vegetables).
With a good knife and working softer, easily cut woods (which I'd suggest should be the case for a child whittler), you may be able to hone only daily, or after each session in other words.
Better news is that if you can learn to get good results by stropping this routine 'resharpening' is the work of just a few moments at best2, certainly less than a couple of minutes including the time needed to get the equipment out and store it again. As mentioned in a few previous Answers this upkeep can greatly extend the period between actual honing, with knives (which are softer than chisels usually) to perhaps weeks.
Some previous Answers for more context and info:
Is the "paper test" actually relevant to sharpening chisels and planes?
How can I tell if wood turning (lathe) chisels are sharp?
When sharpening, how do I assess what grit to start on?
1 Not all hard woods are abrasive (most aren't) but the harder they are the more they'll blunt edges. Some softer woods though are surprisingly blunting, e.g. because of tiny amounts of silica, red cedar being one of those despite being only about as hard as cherry.
2 Experienced stroppers are done in 10-20 seconds.