The answer to your question is neither. The annealer or oven only provide heat to ore-anneal the copper or to drive the solvents out of the liquid enamel or to dry it. The effect is short term or momentary at best unless you are over or under curing a product. If the product is good when it left the oven there is nothing that the oven can do to effect the wire once it is no longer in the oven.
I think your answer may be in your material. Is it a thermoplastic? The difference between thermoplastics and thermosetting plastics is that thermoplastics become soft, remoldable and weldable when heat is added. Thermosetting plastics however, when heated, will chemically decompose, so they can not be welded or remolded. On the other hand, once a thermoset is cured it tends to be stronger than a thermoplastic.
It is probably continuing to cure/downgrade even when sitting on the shelf.
This is not necessarily a problem if you are encapsulating it or putting it in an oil filled transformer. It is a big problem if you are trying to use it for motor windings and coil windings that are not totally encapsulated.
richard