It is probably time to cut bait with this rim and either replace the wheel, or rebuild with new spokes and probably new rim (assuming the flat spot is bad enough).

Over time, spokes can fatigue at the elbows (where they enter the hub). This happens if spoke tension is too low, and so tends to happen mainly on the non-drive-side of the rear wheel. Tension in a given spoke will change somewhat as the wheel rolls around, and if spokes are low-tension enough (combined with loads), spokes can go slack and then re-tension each time the wheel rolls around. This leads to repeated flexing of the spoke at the elbow, and eventually it snaps.

Once you have multiple spokes breaking in succession, it means that most of the other spokes are fatigued and at risk of breaking also. Again, I'm mainly talking about non-drive-side spokes breaking at the elbow.