Every time you go above the annealing temperature, you must anneal again. You cannot skip or skimp on the annealing. You cannot rely on the annealing in the final firing to make your piece durable. Each time you fire a piece you are putting a lot heat stress into the piece. If it has not been adequately annealed in the previous firing, it is much more likely to break on the heat up phase of the firing than if you annealed well on the previous firing.
The annealing at each stage in multiple firings is just as important as the previous one. In addition, pot melts and other high temperature items are inherently more delicate than those fired at their designed temperatures, so more careful annealing (including the annealing cool) is advisable. This is because the compatibility of glass alters a little at high temperatures. For example, you will observe that hot transparent colours opalise in the 900C range. This opalisation in itself will have altered the compatibility a little, because the opalescence alters the viscosity from what it was as a transparent. Other factors are at play too, such as some minor burning off of the colouring metals. So, careful annealing is required to ensure the maximum amount of stress is relieved. You also need to have a slower than usual initial rate of advance for any fire polish or slump firing after any high temperature process.
Even when firing at fusing temperatures, but beyond the tested number of firings, more careful annealing is required. In the case of Bullseye they have tested for three firings, although people get many more firings than that without difficulties. When taking glass beyond the design limits, more care is required in all phases of the firing to get durable results.