Issame,
The reason for the questions about your processes, etc was to get mor information to aid in making suggestions. In making magnet wire, annealing occurs in the enamelling oven and not the pre-annealer. There are a variety of things that can affect springback. You could have adequate elongation and poor springback. At the same time the sheaves or rollers on your oven could be too small and work the wire too much. There is also the metallurgical purity of the copper. Your conductor could be within spec but that could cause poor springback. Additionally there are some sizes of wire where the elongation numbers are hard to achieve but springback values are ok.
there is no one answer to your question however the less information or knowledge shared, the greater the number of possible answers, most of which are probably wrong. any additional information you can provide would help. spectre