TH, given all of the information you have given us...
1.) You think you hit him back
2.) You heard him crashing around in the corn
3.) You heard coyotes ripping into him
My questions are this. Did he act hit when he ran off? A gut shot deer will hunch up. A deer's body language after the shot is crucial in determining if the shot was fatal or if you hit him at all. Could the crashing around in the corn have been other deer running off at the sound of you on your cell phone? Were the coyote howls coming from where you heard your deer crashing around in the corn?
If you're certain that you hit him, then at this point, it would be unethical to sit again and wait him out unless you've exhausted every opportunity to recover your deer. You need to get out there ASAP to attempt to recover him. I'd start where you thought you heard him crash. A gut shot animal won't have much blood so if he's not there, he'll either be in the thickest cover on the property or at a water source.
Good luck!