Stiff springs are a good way to transfer load from one point to another, but two springs meeting at a single node is an unstable configuration since the stiffness for the single node to move laterally in the plane of the two springs is practically zero. If you had three non-coplanar springs, that would be a stable configuration. You can artificially add stability by adding a Displacement BC to that one node to set the lateral deformation to 0. You may need to create a Coordinate System to define the lateral direction.
The title of that analysis in the image above mentions that Large Deflection is On, which is a requirement to get accurate forces in the springs.
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