If that cover plate is steel, it could be welded. If its polymer, I'm sure there's something that'll hold it. There's not a lot of stress, or pressure there. So a patch should last awhile. Giving time to find a replacement. And a skid plate.
My vote would be either the speed sensor, or sending unit. Whatever it uses down in the wheel, or transmission. Or fouled wiring from sticks, or branches. I'd start by giving a good look at the wiring. Then figure out where the speed sensor is. I could see water, or mud causing the problem. If the readout is moving at all. Then it seems like that part is working.