This question is interesting, because it points up the fact that a scientific theory can experience a reduction in its scope and explanatory power without being rejected as completely wrong. In addition to the answer given by sand1, here are some other examples that might fit the bill.
Dalton's theory of atomism. According to Dalton, all matter is composed of atoms of the chemical elements. This theory has considerable explanatory power. It succeeded in accounting for the chemistry that was known in Dalton's day, such as the fact that substances can be reproducibly decomposed into the same elements, and that elements combine in fixed proportions to make compounds, etc. Dalton's theory was that atoms are indivisible and the elements are immutable, and that all observable changes are the result of atoms separating and combining. The latter turned out to be incorrect. Atoms are divisible and elements can turn into other elements by radioactive decay. Nevertheless the core idea remains that atoms are the fundamental particles that constitute chemical elements, and chemical changes can be explained in terms of atoms separating and combining. We need other theories to explain nuclear changes.
Conservation of mass. Classically it was thought that matter was conserved. There was strong empirical support for this, and it appeared to hold universally. Later it was shown that in relativistic settings the energy associated with the mass of a body can be converted into other forms of energy. The principle is still useful, however, just not universal.
Charge, parity and time symmetry. It used to be thought that all of these forms of symmetry held independently. Later we learned that there are exceptions to each of them, but the combination of all three appears to be symmetric. This means we still have a working theory of symmetry, but it has less scope and is weaker than having three separate ones.