I'm not familiar with how or what those radios do to self-test the antenna ground, however typically what you want is to have is the antenna (it's bracket) mounted directly to a substantial mass of metal to act as a ground plane (it doesn't necessarily have to be the center of the roof, though that would be ideal). If you have a large metal roof rack, typically that can work well for mounting an antenna, as can mounting it to the vehicle's rain gutters or a hood-lip mount or to the side-panel of the body (preferably with at least 60% of the antenna's length clear of the body in any case).
What usually doesn't work well is mounting the antenna's bracket onto a metal mast or post sticking up from your bumper or spare tire carrier, nor does mounting the antenna directly to the bumper itself (the rear one in particular, due to the body blocking most or all of the antenna). Similarly, mounting to a tire carrier swingout itself can be hit or miss as well (same goes for tail light brackets).
If you can post a pic of how it's actually mounted, I or someone else might be able to provide you a more direct answer.