To followup, while tying DIN to DOUT together did help with whatever interference was occurring on the the DIO pins, I hadn’t realized until recently that there was still interference on the one analog signal. I just hadn’t needed that part of the system until recently and assumed that the problem had been solved.
Tying DIN and DOUT together and to ground, as John suggested, on both xbees, solved this issue. It now seems like the problem is completely resolved.
This thread helped me out just now. I was having very similar problems with trying to drive a 74HC595 shift register (SIPO) from pins AD0 thru AD3 on my XBee.
Adding a ground connection to both DIN and DOUT removed my cyclic resetting problem. For me it was 6.5 seconds between resets when using a breadboard to prototype the design.
I’m still suffering with other problems now though - occasionally one of the IO pins looks like it’s not toggling when it ought to be, maybe 1% of the time.
In any case, if you’re not using serial data features on your remote radio, then it looks like a good idea to tie them hard to GND if you can. Worked for me at least.