Further to what has already been said, I'd like to quote from my latest bed time reading

The Bicycle Wheel by Jobst Brandt.
"In the bicycle wheel, wires replace the rigid spokes of wooden wheels. Although wires are strong, they cannot directly replace wooden spokes that carry loads in compression.
In order to work, wires must be tensioned to prevent their buckling under load. With tension, wires can support compression loads up to the point where they become slack. "
"In a broad sense, wheel failure means that through some defect, the wheel becomes unusable. For example, it may become so misaligned that the tire rubs on the frame or the brakes drag. Or it may get dents in its rim from hitting a curb or riding with insufficient tire inflation. Most wheels fail gradually by losing alignment, and this deterioration can be controlled. On the other hand, the sudden collapse of a wheel is caused - with few exceptions - by excessive side loads."
Basically, unless the OP hit a curb or a pothole and damaged the rim, the problem he has is that some spokes on on one side are looser than on the other side. Correcting this tension imbalance should fix this particular problem, however, the OP should make sure all spokes are tension balanced. In rear wheels or wheels with a disk this is a little more complicated to explain and that is because of the dish of the wheel which means one side is supposed to have spokes with less tension than the other side. In those cases the thing to do is not to look at balancing the tension difference on both sides but to tighten the spokes on the opposite side of the buckle until the wheel is true again. Again, balancing the spokes tension on each side is recommended.