Today, the once mighty colonial empires of Europe consist mainly of a bunch of Islands, French Guiana, and some other places. What would have had to happen for large scale colonialism to remain into the 21st century?
IMO: The triumph of reactionary authoritarianism over democracy. The eventual demise of colonialism was implicit in the premises of liberal democracy, as it existed in 1900. The rising superpower, the U.S., was deeply unsympathetic to colonial rule. The Versailles settlement in Europe elevated national self-determination to a supreme principle - then restricted it to whites, causing widespread resentment. That contradiction was going to bring down colonialism, eventually -
if liberal democracy remained the dominant ideology.
However, liberal democracy might have foundered in the mid-century crisis. I have envisioned an alt-WW II in which a deeper economic crisis spawned outright Red rebellions the U.S. and Britain, leading to quasi-fascist regimes in those countries. The U.S. and UK allied with Germany and Italy to crush Red France, the USSR, and their ally-of-convenience Japan.
After the War, the colonial powers (including France, where the victors installed a reactionary government), ruthlessly suppressed all independence movements, and this world order persisted into the 2000s.
It would be milder, than its 19th and early to mid 20th century counterparts.
I think it has to be harsher than in the early 20th century. For a long time, most colonial peoples submitted quietly to rule by the colonizers, because they had always been governed arbitrarily - by locals, near outsiders, now over-seas strangers, what was the big difference? In the 20th century, they began hearing about self-determination, democracy, and the principles of the American Declaration of Independence. And they realized they didn't have to submit. They demanded autonomy at the least, or formal independence, and liberals (in the classic meaning) agreed.
From that time on, colonial rule could have been sustained beyond 1960 only by harsh repression, backed up by authoritarian (and at least mildly racialist) attitudes in the colonizing countries.
There is a sort of utopian alternative, in which the colonies become fully autonomous but still non-sovereign dependencies. I don't think that is really plausible, because of the example of the "white Dominions".
As of say 1850, Canada, Australia, and New Zealand were
colonies. By 1950, they were
sovereign countries. In 1914, Britain's declaration of war on Germany automatically applied to them, as much as to India or the African colonies or the West Indies. In 1939, they were just as loyal to Britain, but they issued their own declarations of war. So did India, actually - though there was great resentment on the part of the Indian Congress that it was done unilaterally by the Viceroy.
(It would be interesting to know when the Dominions began establishing their own diplomatic relations with, for instance, the U.S. - or say Italy.)
By 2000, all colonies except the smallest would insist on being sovereign.
A PoD to establish more permanent colonial rule would have to be long before 1900, IMO.