Is it permissible to continue supplicating for Allah to provide me with new teeth in place of the ones I lost, even though that is usually considered impossible by conventional wisdom and reason?

Deciduous teeth fall out and are replaced by permanent teeth. However, if permanent teeth fall out, they do not grow back, and their return is usually considered impossible. This should not cause you to lose self-confidence. Instead, you should occupy yourself with acquiring knowledge, remembering Allah, reciting the Quran, and befriending righteous people. They will assist you in obedience and love you for your obedience to your Lord, not for your appearance. Strive in supplication, asking Allah to grant you beneficial knowledge and righteous deeds. So supplicate: "My Lord, increase me in knowledge," and "O Allah, help us to remember You, to be grateful to You, and to worship You in a perfect manner."