Is it permissible for a Muslim woman to wear the niqab, then remove it, then wear it again, and so on, based on the change in her conviction between its obligatoriness and its Sunnah status?

If a woman is knowledgeable and capable of examining evidence and weighing different opinions, then she acts according to what she finds most compelling, even if it contradicts her previous view. If her ijtihad (independent reasoning) changes repeatedly, she must act according to her latest ijtihad. However, if she is a muqallidah (a follower of a school of thought), then she acts according to the opinion of a scholar whose knowledge and piety she trusts, and she follows the opinion of the one she considers most knowledgeable. It is not permissible for her to switch between opinions capriciously.