165 yards with a .17HMR is very reasonable !
I have shot my fair share with my .204, "most" one shot one kill, but there is always the exception(I rolled one and thought the same thing-never found him).
I would try to take head / neck shots on coyotes if using a .17HMR.
No need to take your 44 mag to shoot coyotes !!!
Keep your chin up.........................