A 3 foot section of the plywood subfloor under the carpet in the center of our backroom is lifting. It does not appear to be the whole sheet but two or three of the plys along one edge. Can the carpet be cut and repaired without redoing the whole room? Are there any special nails that could be installed through the carpet to hold the plywood together? Does anyone have any other ideas?

The carpet can be lifted and reinstalled once the removal and replacement of the sub flooring is done.

Is there a door opening that has heavy foot traffic over that area?

Is there moisture anywhere near this area?

Finding the reason it has happened will better suit your type of subfloor replacements(ie:Plywood,OSB,etc)