They are so similar it's hard to tell the difference.
To say "I don't find it" is to say you are still looking, but, as yet, you have not found it.
To say "I can't find it" is an admission of failure.
Generally, we say, "I can't find it" but I have learned, with my current boss, to say "I don't find it yet..." because he will come in and point to it and then I can say, "Ah, yes! There it is! Thank you!" But when I say, "I can't find it" it looks like I am incapable, and have given up.
I don't know if it makes any difference, but it works for me!