Is the standard enthalpy of formation always non-positive?
You'v answered the question yourself.

In general, any enthalpy of reaction is the measure of the energy remainder after breaking the bonds (positive) and what energy we got back from the formation of the bonds (negative). 

The net sum can be positive or negative, and it depends on what the reactants and products were. As you correctly said yourself, $\ce{NO}$ happens to have a positive standard enthalpy of formation because, as experimentally determined, more energy went into breaking the bonds of reactants than what we got back from forming the products.

So,


  Is the standard enthalpy of formation always non-positive?


The answer is no.