There are two reasons behind this that I would wager.

The first is the simplest. The older a thing is the more likely it is to be lost, whether natural degradation, accidents, being left somewhere obscure or being destroyed intentionally.

The second is related to the mechanics of the first. During the 16th century there were a lot of ceremonial armour pieces made, as the cult of princely ceremony grew. This was a time of great wealth at princely courts and of showmanship. In the words of Diana Davis Olsen; "Sixteenth-century scholars can point to this period as the apogee where armor became works of art, created by a handful of skilled artisans, such as Kunz Lochner and the Negroli family. Parade armor would not only be decorative, but would come to be used as a medium to make specific statements among Europe’s most elite citizens." (The Visual Language of Power: The Role of Equestrian Armor in Renaissance Europe, 2011). As she points out, this armour was mainly used for parades, as well as tournaments. These ornate high-class pieces survive because there were not worn that often, and were replaced if too tarnished. And they were kept around rather than gotten rid of because they were so expensive and prestigious.

Indeed, during this period an increasingly large amount of professional bureaucrats and gentry politicians were getting in on the status game. So we have examples like the armour of Thomas Sackville, 1st Earl of Dorset, who probably never wore it. Sackville was mainly a politician. Yet this armour is both gilt and blacked (the blue bits are tarnish), in a fine pattern which would be expensive. Why? Because he wanted to be able to say he had one. He was the first in his line to hold a title as both 1st Baron Buckhurst and 1st Earl of Dorset. This meant it simply stayed on display, clean and well-preserved as a family heirloom representing their entry into the ranks of entitled nobility.

So in short we have a bunch of largely-ceremonial, expensive and beautiful armour from the 16th century that stayed in good condition and was kept around, because it was so beautiful and expensive. It's similar to the way classical Greek and Roman scholarship and literature survived best if it was copied, referenced and redistributed in the Medieval and Early Modern. Things of value are kept.