Can new Divaydesams be created and/or existing ones derecognised as such?
Divyadeshams are the sacred places for all the Sri Vaishnavas.
The list can be only increased or decreased when the alwars and their poems are increased or decreased. Divyadesam is a place to which Alwars have sung the praise of Lord Vishnu's form ( this can be any of the five forms) present there. There are 108 Divyadesams for which Alwars have sung praise in their poems. 106 are present on earth and two are not. They are the milky ocean and Paramapadam, the highest abode of Lord Vishnu. Singing the praise of the Lord and compiling the Nalayira Divyaprabandham are the important reasons Alwar were born. As the task is completed, there wouldn't be new alwars similarly no new Divyadeshams too. I explained the reasons why there are 12 alwars and not anymore new alwars in this answer of mine. As there are no new alwars, there wouldn't be new addition or removal of the existing places from the list.
Every new temple constructed has its own importance and uniqueness but they will not be equated with 108 divyadeshams.