I found this in my company's operation manual. I guess I should have started here in the first place but thought I'd include it in this thread for information purposes.
Failures and Associated Actions
In general there are three possible responses to the failure of any system,
instrument or element during the approach.
1. CONTINUE the approach to the planned minima.
2. REVERT to higher minima and proceed to a new DH (above
1000ft).
3. GO AROUND and reassess the capability.
The nature of the failure and the point of its occurrence will determine
which response is appropriate.
As a general rule, if a failure occurs above 1000ft AGL the approach may
be continued reverting to a higher DH, providing the appropriate
conditions are met.
Below 1000 ft (and down to AH when in CAT III DUAL) the occurrence of
any failure implies a go-around, and a reassessment of the system
capability. Another approach may then be undertaken to the appropriate
minima for the given aircraft status. It has been considered that below
1000ft, not enough time is available for the crew to perform the necessary
switching, to check system configuration and limitations and brief for
minima.
In CAT III DUAL, in general, a single failure (for example one AP failure or
one engine failure)below AH does not necessitate a go-around, but a go-
around is required if the autoland warning is triggered