This is a staining job not a finishing job. You are also doing an experiment. Think of finding this answer to be another variable.
I'm sure at some point, the stain will be mostly unnoticed, and this point will be different depending on the darkness of the original color you begin with (Oak vs Walnut). But ultimately the stain will continue to 'work' it just will get to the point it is worthless for any obvious change to the wood, you're just making it wet then.
But I would guess, depending on the original color, you can dilute between 100% (1:1) to 400% (4:1) water to stain and still have some color depending. Non-wood color stains I think can be more diluted, say green or blue, while an 'oak' stain might be fairly useless at %50 (1:2).
What matters is what color you start with, and how much color you want to make a difference. Since you are already experimenting, you'll find this limit. Just make small samples for your tests (and good notes!)