First consider the other three pillars and how they link with each other. Each of the three pillars has defined roles with limited or very specific powers (or lack of)  over the other ones, they are also civilian based and therefore would lack the resources to overthrow the other pillars with force. Any constitutional power given to the military would be backed up with force potentially giving dominance over other pillars (leader X rules at the pleasure of the military).

In terms of the military defining a role is rather difficult any definition that is too vague allows them to jump into any breach with full force and anything too specific and then there won't be much point
possible definitions:

 1. "To defend nation X it's principals and values" (ECT). This is rather vague perhaps defining some principals and values would help but anything like this is so open to interpretation that they could easily use it to start a civil war at their convenience
 2. "To ensure [some other pillars] are acting in the best interests of the people" again vague and empowering the military to act whenever it suits them and requiring that the government keeps the military happy
 3. "Defend nation X again external military threats " very specific provides no real powers above what the military has anyway

Giving the military a day to day role in the running of the nation is rather difficult i.e. there is no obvious role for them in making most legislation such as tax reform ect. Where as the other pillars have well defined roles in these situations.

Wring the military into the constitution legitimises any unofficial power they may have had and this may undermine attempts for a country to be democratic.