I'm not sure if there is a story behind it or not.
The term "re" means again, its happened before, and its happening again, so at least twice. The term "approach", means to become near to a "thing", or becomes closer. I hope that helps, if it doesn't let me know
Whilst they may share a common latin root, the meaning of this word is seemingly derived from the Old French "reproche" - "to blame, bring up against".
Also, consider that in this case, "re" is not "again", but more true to the latin "re", which means "the opposite of", and the latin root "probare" - prove to be worthy.
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Reproach \Re*proach"\ (r?-pr?ch"), v. t. [imp. & p. p.
Reproached (-pr?cht"); p. pr. & vb. n. Reproaching.] [F.
reprocher, OF. reprochier, (assumed) LL. reproriare; L. pref.
re- again, against, back + prope near; hence, originally, to
bring near to, throw in one's teeth. Cf. Approach.]
1. To come back to, or come home to, as a matter of blame; to
bring shame or disgrace upon; to disgrace. [Obs.]