There is a common assertion that you need to extend the annealing - or temperature equalisation soak - on each firing after the first.
The rationale for this is never fully explained. Possibly it comes from the fact that you need to reduce the rate of advance on already fused pieces over the unfused lay-up. It is also possible the rationale is that since you need to slow the rate of advance, so you need to extend the anneal soak.
However, if this is the rationale, it is rarely followed through on the anneal cool in the detailed schedules in these instances. Generally, the cool on extended soaks is the same as on the first anneal, but extending the anneal should apply to the cool too, according to this kind of rationale.
At normal kilnforming temperatures, the anneal for the determined thickness (allowing a doubling of thickness for tack fused pieces) is suitable even for multiple firings.
Once you go up into the temperatures for melts, there is reason for more caution. There is the risk that the high temperatures – especially for hot coloured opals – may induce a little incompatibility. A longer soak for these may be considered desirable. Even so, this does not need to be extended at each subsequent firing.
You are annealing at each firing for the thickness – actual or calculated – of the piece, not for the number of firings.