Smart Key/Keyless issue: works randomly, different handles respond, someting

I’m having an issue with the Smart Key/Keyless system in my Gen 2 Prius and I’m wondering if anyone has experienced something similar.

Symptoms:

The car starts fine with both keys (both when inserted and without inserting – the transponder is recognized).

The problem is with locking/unlocking the doors using the handle (keyless) and sometimes with the remote buttons.

The LED on the key fob blinks when trying to lock, but the car doesn’t lock.

Sometimes the driver’s door handle works, sometimes only the left rear door handle works, and sometimes neither.

Sometimes the trunk button will lock/unlock, and then it stops working again.

Sometimes the keyless works perfectly in the morning, but after a few hours of parking or even after a short drive it starts acting up.

Occasionally, the handle button only works if the fob is close to the rear antenna (near the rear door), but not from the front.

On the dash, I sometimes see the orange “car with a key inside” indicator (not the golden immobilizer one) blinking.