Wouldn't the solar wind continuously impart some momentum on the field generating station, eventually pushing it out of L1? I don't doubt we could generate a good enough field, but the continuous station keeping might be tricky.
It wouldn't be a problem for a species with an active space economy to keep a few satellites at L1. Should the species no longer have active space travel then eventually the planet would be screwed though, but how long is "eventually", and how long would the satellite have to be in place before the goal is met.
As a species we struggle do 5 years projects, let alone 500 or 5000 year projects.
I would see this sci fi movie!