Q:

Can we use another word instead of "Might" in Optative Sentence in Narration?

For example 
They said,"long live our democracy!"
They wished that their democracy might live long !
whether the word 'might' in this sentence  is representing possibility?

A:

This is quite complicated. 
It does mean possibility, but not in the sense that people usually use might today.
In current speech, might is used as a tentative possibility ("I don't know if it is, and I don't think it is very likely, but it is possible", or something like that). It tends to be more doubtful than may. 
This is an older use, where might is formally the past tense of may: past, because it is indirect quotation: "May our democracy live long" -> "They wished that their democracy might live long". 
The sense of "possibility" here is not "it is possible", but "we want it to happen [but cannot be sure it will]".
May is still used in this way, though it's a bit literary; but might is not often used as its past tense. 

