What are some mathematical problems which have been forgotten?

The n-body problem dates back to the ancient Greeks and was once considered the key to understanding the movement of the planets, and, by extension, the very nature of the Universe.

A "geometrical" (i.e. exact) solution was always hoped for and expected, but the desire to compute orbital motions in practice led to the development of numerical methods; in the meanwhile, it was discovered that the case $n>2$ is chaotic (an early motivation for chaos theory).

Both numerical analysis and chaos theory have since dwarfed the original problem in terms of the amount of research effort dedicated to them, and while it's difficult to say that the n-body problem is "forgotten" (if it were, we couldn't be discussing it) I'm not aware of any substantial theoretical work (let alone progress) done on it for several decades now beyond what is already covered by the more general field of numerical methods.

Add to this the fact that the relativistic version of the n-body problem is fundamentally different from the classical formulation, leading to a solution for the classical problem being of much lesser interest in today's context of large-scale celestial mechanics than it would have been two centuries ago, and you have this once monumental problem being now reduced almost to its historical importance alone.