Why is the word נערה typically written in the Torah without the final ה?

The first noteworthy point here is that there is only one instance in the Torah where na'arah is spelled with a final hey. This appears in Deuteronomy 22:19. All other instances (Genesis 34:3, 12) are without a final hey.   

According to the Zohar (Parshat Bo) a female who has not yet developed her feminine capacity is referred to as a na'ar without a hey. Rivkah was less than three years old (according to many opinions) when she met Eliezer and therefore is referred to as a na'ar rather than a na'arah (See Midrash Zuta to Bereishit 34:4 as well). 

In other places in the Torah, the absence of the hey in the word na'arah indicates that she had conducted herself in a manner not befitting to her. For example, Dinah (daughter of Yaakov), who "went out to see the daughters of the land" and was then seduced by Shechem. The Torah is critical of her behavior and demonstrates this by removing the final hey. 

Along these lines, Na'ar (נער) is of the same numerical value as shoteh שוטה (fool), and one who does something that is a shtus (deviant) is considered a na'ar - a fool, and thus the Torah is indicating that her behavior was foolish (Ba'al Haturim to Genesis 37:2 - Rabbeinu Yakov ben Asher, son of the Rosh).

In Deuteronomy (ibid), all other references to the girl in that discussion are made without the additional hey, because again, there too the girl - at that point in the development of the story - had conducted herself inappropriately. Only once she has been established as a pure victim is she exonerated and referred to as a na'arah, complete with a hey.