Though prostration was the normal mode of prayer in Judaism from ancient times and Jewish Law (Halacha) requires it (particularly during Tachanun) it was abandoned during the middle ages. Bowing on the knees and prostration during Tachanun may have been done away with due to a reference in the Rambam which states that if a man is as great as Yehoshua ben Nun then they should not prostrate. The Rambam doesn't explain this statement but the later Aruch HaShulchan explains that for in so doing he may lead klal Israel astray if by chance his prayers are not immediately answered. In other words, someone who thinks they are as great as the prophet Yehoshua (Joshua) is exempt because if during their prostration their prayers aren't answered then people will lose faith in God. Of course, this exemption relates only to great Chakhamim (Sages) and there are no Sages as great as Yehoshua ben Nun in our day. It would seem that the minhag of not prostrating developed as a result of some Rabbis who thought very highly of themselves and didn't prostrate. Resultantly the laity, upon observing the Rabbis lack of prostration, ceased prostrating themselves perceiving that this was the correct mode of prayer.
It is also probable that prostration in prayer was forbidden to Jews during Islamic rule just as the 16th century Sultan Murad III forbade Jews to continue their custom of wearing the turban. There is likely several reasons that altogether removed the custom of bowing and prostration from Judaism.