Persistent Idle Fluctuation in Toyota Corolla 1.5

I'm having some issues with my Toyota Corolla 1.5. The idle seems to fluctuate constantly, and I've noticed a decrease in traction and some juddering between 1000 and 2000 rpm. This issue continues to persist despite numerous visits to two separate dealerships, with no resolution in sight. Despite a temporary solution being implemented via a software update, the problem resurfaces upon rebooting the vehicle.
