Sorry it's kind of late for me to see this but...

What brand are they? Is it for the 2-bolt cleats or 3-bolt?

If you contact customer service / warranty for most brands, they will send you a replacement plate. If it's 2-bolt, I think they're all the same, so maybe you can just find the plate at your LBS. I think those commonly come loose, so it might be an easy find. If it's 3-bolt, those, too, are probably the same, but if your shop is like mine, they won't have a clue what to do. So, just ask the manufacturer to send you a replacement part.

The problem I had with one of my shoes is that the plate had come loose such that the screw receiver part would just spin wildly inside, giving no resistance for the screw. It would start to be threaded, but once it got close to tight, the thing would just spin, and the bolt wouldn't get any tighter. I could put pressure on the plate from the inside to get it almost tight, but it wouldn't last long. So, since mine was loose, it was really easy to get it out. If yours isn't, it might take some prying for the 3-bolt style. The 2-bolt should be readily accessible. You can find all of them under a flap that is cut into the shoe under the removable insole.

I have Specialized 3-bolt only road shoes, and they sent me the parts plus some extras. Also, if you need the 2-bolt kind, let me know, because Specialized accidentally sent those to me first (because they messed up), so I have a worthless set of cleat plates around here somewhere.....