Is it permissible to marry a girl who has lost her virginity and claimed repentance, while fearing that my marriage to her might be a divine punishment for a sin I committed against my neighbor?

The question is unclear. If what is meant by "covering her" is not exposing her and spreading news of her sin, then this is obligatory, especially with her repentance. Verifying the sincerity of her repentance is up to Allah, and people are commanded to act based on apparent signs.

If what is meant by "covering her" is marrying her, then this is permissible, provided that signs of her repentance from immorality are evident. If you fear her repentance is not sincere, then forgo marrying her and seek someone else of religious commitment and good character. But if signs of righteousness and remorse appear on her, then accept her as a wife and cover her.