the longevity of amorphous metal I gathered that many of amorphous solids are made by quickly cooling the liquid material, thereby giving it no time to form any long-range order (crystallinity). So it makes a perfect sense that when high heat is applied to amorphous solid, it will regain its crystallinity, and will no longer be glassy.

But is this behavior non-continuous? That is, can sustained low thermal excitation give rise to the crystallinity in amorphous solids given enough time? Or is there a threshold temperature (or a level of thermal/mechanical excitation) below with no excitation can bring back the crystallinity?
The answer to your question is no in general. Because amorphous metal is usually an alloy rather than a pure metal. These alloys are made of atoms of largely different sizes, which results in low free volume and higher viscosity (compared with other metal and alloys) in molten state. The viscosity hinders the atoms movement to form a crystal.

So, the significantly different atomic radii of the components that constitute the amorphous metal (about 12%) favors the high packing density and low free volume. This leads to a complex crystal units with higher potential energy and lower chance of formation. 

Accordingly, I think that even if we heat an amorphous metal above a threshold temperature  and let it cool slowly, we won't have a conventional crystalline structure. At best, we get regions of some order.