I see. I played around with it a little after configuring the GPS with FasterFix, and found that I have no problems keeping a GPS lock when the phone is charging, but it will not keep GPS lock when it is running on battery alone. I think this is due to the fact that I have "Stay Awake while charging" checked in Dev Options...so it won't go to sleep and turn the GPS off.
But, shouldn't Google Nav force the device to stay awake while it's running whether it's running off battery or not? I think the problem is that Navigation isn't doing that...or more likely, that there is something interfering with it forcing the device to sleep when the screen is off as some sort of power-saving measure. All my "power saving" tools in ROM control are turned off though...