The issue may not be related to the material loosing strength, but an issue with the quality of the cut edges.

Best regards - Al

IJR...to answer your first question, for mild steels the strength does not change except in a very localized sense which might become either quenched or annealed, depending on the cooling. Neither is significant in the whole scheme of things for flame cutting. Essentially, flame cutting is not much different than welding in its affect on the base metal. It creates a similar heat affected zone (HAZ).

Agree with gtaw that it is probably a visual rejection based on the way the flame cut looks. Field cutting is usually done with expedience....with larger tips and higher oxygen pressure....just to literally "blow and go". You might want to specify or suggest a smaller cutting tip to give a "finer" cut appearance.