SAS:
"why might an engine fail on final?"
Well if the engine is at the back and you were to inadvertently pull mixture rather than carb heat
... Someone I know intimately did this many years ago in a Long-eze. They noticed when the aircraft started to sink and throttle didn't have any effect - fortunately the air brake is effective so by raising that the runway was made, engine restarted on the roll and nobody every knew about it (pssst, so keep it a secret
)
"Lifting and raising gear and flap, causes more drag than just leaving it extended" - this may well be true for some larger types but I doubt if it's true for an Arrow. The gear and doors don't change their orientation compared to the airflow and nothing else pops out into the breeze during the process; so where would the extra drag come from? Raising the flaps certainly causes short term sink but there is a nett gain in glide angle provided the speed is OK so may well help things early in the approach - it also means you may be able to use them again to jump obstacles.
Stiknruda:
at idle the prop is on the fine pitch stop and is unlikely to respond to prop lever movements (although maybe an electric one would).
The over-riding message through all this should be to fly the aircraft at the correct speed and to make a decision about the options - not to keep pointing hopefully at a runway that you may not be able to reach. A controlled arrival in the best available place is very much preferable to an uncontrolled arrival at somewhere chosen by the gods of aerodynamics.
HFD