Those are called mullions or muntins. They are repairable, if you have the time to do it yourself or the money to hire someone else to do it.

Depending on the age of the room, it may be cheaper to replace the windows and frames, but they look so lovely on the inside, it's a shame not to repair them.

Do some internet research on wood repair, or buy some books on how to do it. There is a famous book called "Working Windows: A Guide To The Repair And Restoration Of Wood Windows" that explains how to repair old windows. There is a lot of good info on the Old House forum here.