That's something of a bugger in these type of jobs alright.
Here are a few things that *might* be the problem. (with solutions)
1. The bridge plate is very large and dissipates heat rapidly, hence, it's a proper bugger to solder onto. Try "Spot Heating" the underside of the plate with the soldering iron, or, better yet a small blowtorch, then rapidly soldering (just a quick "tack") the wire (pre-tinned, of course) on, and then finishing it up with additional solder.
2. The plate is plated with chrome, and the solder won't "take" on this surface. Simple enough. Whack a patch of it with some heavy grit sandpaper and solder onto the resulting "wound".
3. Your solder is, to use a technical term "shitee". Buy some better solder. No idea what "Better" is. I'd ask a plumber.
That's all I can think of. Apart from a mad notion involving a drill, a pop rivet and a spade terminal, should all else fail.