not dropping down to the small ring is more of an issue with the cable not releasing fully or having a worn out chain, assuming the FD hasn't moved.
It's going the other direction, small to middle. Fine going from middle to big.
most times those inline adjusters will slip, so check that they are properly turning.
turn clockwise to tighten cable and counter clockwise to loosen, just like the adjuster barrel on the RD.
Clockwise standing on the same side of the bike as the front shifter? With the tops of the bars pointing to your belly, clockwise looking down the cable. How would I fix it if it's slipping? Replace?
Maybe I'm missing something, but this appears to be the only place to adjust the cable. Other than resetting it at the derailleur.