Glubb's claim is nonsense fabricated to further his arguments. He gives a very limited set of examples from basically just Europe and western Asia and it's still riddled with holes, like including the Roman empire (almost 500 years even if you don't include the eastern half, which lasted another 1,000) and Alexander the Great's empire (which famously fell to pieces upon his death). It's not even clear how he chose the start and end for several of them

I'm not meaning to come across as mad at you or anything, I don't even know of you got the claim directly from Glubb's work or heard it elsewhere