In heavily hunted areas, use handcalls.
I'm not picking on Foxpro/Luckyduck, but, every new guy that uses a Foxpro/Luckyduck, is using the exact same sounds, meaning the exact same Cottontail/Jackrabbit/Woodpecker sound comes out of most every Foxpro/Luckyduck.
If the new guy gets busted while playing the Cottontail on the Foxpro/Luckyduck, that coyote might be much harder to call in a 2nd with the Cottontail on the Foxpro/Luckyduck.
My experience has been, once I get barked at, I've been busted, so I pack up and go somewhere else.
As others have posted, sometimes, coyotes just won't respond, even though they hear the call.
If you can, go to a large State Park or other open area, where you can't hunt coyotes, and make some stands there. If you start calling those 'park' coyotes in, you know you are on the right track. Watch how, and from where, they approach, and try to figure out why they came from 'there' and not where you thought they should come from.
And, of course, read these current and past posts. This place is a wealth of knowledge, with many, many excellent coyote hunters on it.
Good luck, and keep us posted.