Is it permissible for a worshiper who invoked evil upon himself, and remembered two weeks later that he was not in a state of ritual purity at the time of the prayer, to repeat his prayer for fear of apostasy and dying outside of Islam?

You are not required to repeat your prayer unless you are certain that you performed it without ritual purity. Mere assumptions and doubts do not necessitate repeating it. If you repeat it after being certain of its invalidity, then no harm will befall you from what you invoked upon yourself, because an invalid prayer is as if it was not performed.

Invoking curses upon oneself is not permissible, whether it is immediate or conditional. Whoever does so must repent and seek forgiveness. Your fear of disbelief due to this invocation or repeating the prayer is a whisper from Satan. The best cure for whispers is to disregard them and not pay them any attention.