Great question! This happens most frequently with my A. seemanis. I agree with the posts above, the tarantulas are either not hungry or not interested but most definitely bothered.
I would leave the crickets in the cage for up to 12 hours depending on the temp./hum. of the cage. If it's really hot and humid in there, it'd be a safe bet to remove it more quickly to help lower the chances of mold/mites. Most likely the t isn't going to go back for it. I'd also be wary about dead crickets/remains in the water dish. Remove it to prevent, again, mold/mites.
In my experience, if a tarantula doesn't eat a cricket in the first 30 min. then it's not going to eat it, so I remove it a try again the next day. If it again refuses it, I assume it's in pre-molt. Hope this helps some.