DAt also used for indicating purpose or intented goal. From this point of view,in meaning, -a/-e is very close to "için": sevmeye = sevmek için (as in the example: sevmeye yürek gerek - sevmek için yürek gerek) So back to your example, "neye korkuyorsun - sevmeye" could also be "ne için korkuyorsun - sevmek için." 

I think it is:

-a/-e => için

neye => ne için

niye = niçin

p.s. you don´t have to thank me for my contribution here  

Nişanyan´s dictionary is not the only source actually. It is popular because it is online. I think TDK should work on this online dictionary issue.  If i will have chance to  check my etymology books i will let you now.  

But  now lets check from another point. 

In Turkey Turkish we are in doubt if  it is coming from ne-y-e or ne diye so let´s check some examples from other Turkic dialects, 

In Turkey Turkish        it is  niye    ne+e (dative)  / or /  ne + diye?

In Uzbek Turkish         it is  nega    ne+ga (dative)

In Kazakh Turkish        it is  неге (nege)   ne+ge (dative)

So above we can see one example from  each dialect group ( Oghuz, Qarluq, Kipchaq ). And according to the other dialect examples,  i think it is clear that niye is coming from ne+e. 

We are glad you are back at this god-forsaken website.

Hey,

I checked the dictionary (Türkiye Türkçesindeki Türkçe Sözcüklerin Köken Bilgisi Sözlüğü, Tuncer Gülensoy) and it is written like this;

neye ~ niye ´Bir olayın sebebini ve amacını sormak için kullanılır´

< ne [> i]+y+e