On a single-handed yacht, the main backup is the primary autopilot. Not only is this assuming that you have an autopilot, but that the failure of the primary unit should have easy access and connection to an alternate autopilot.
On a large vessel, many are under the false illusion that the failure of an autopilot simply requires manual sailing until time permits to conduct a repair.
We have first-hand experience with autopilot failure on a 2-crew sail from Tonga to Fiji. During this 4-day trip, the autopilot failed on day two, which left us with 2 days of sailing manually. The autopilot was unable to hold course due to boat speed and wind, disconnecting when speed (>9kts) and wind (>25kts) were exceeded.
Normally, autopilot failures occur at the worst time (night in unstable weather, as was the case with us), making repair or reconnection of a second unit difficult, if you have that alternative.
While we did carry a spare autopilot drive unit, the drive unit was located behind the helm wheel and connected via a sprocket and chain to the main steering.
In swells of 3 metres with wind over 20kts, we could have turned into irons, released a drogue, and worked on the system. This became are last resort.
Instead, we chose to hand-steer and decrease shift periods to reduce fatigue levels to a safe anchorage.
On a side note, I had very high confidence in the other crewmember. This is important as it allows you to get good 'stage 3' sleep during your off-shift period.
Hand steering and somehow starting to search through your spares to repair or reconnect a second unit is near impossible. This lifts your single-handed sailing safety risk up many steps. Stress levels climb, and the mind processes start to suffer exponentially.