Shimano canty's?

Check the round gray plastic covers where the brakes attach to the frame. Do you see or feel a crack?
That's common with those older Shimano canty's. The gray plastic cover contains the return spring. When it cracks, the return spring loses it's tension and that brake arm doesn't function properly anymore.

The "A" solution is to replace the brakes. I generally replace them with lower end Shimano V-brakes. You have to replace the brake levers too.

The "B" solution is to replace the spring covers. Shimano used to warranty them at no cost to bike shops but I don't know if that's still true today or not.

The "C" solution it to wrap a zip tie or some mechanic's wire around the cracked spring cover.