I grew up just outside New Orleans, although I am not of Cajun or Creole descent. My understanding is that Cajun French largely died due to a number of factors, many of which, like educational restrictions and population pressures, were already touched on here.
A few more recent factors that I believe have contributed to the decline in Cajun/Louisiana Creole French have been the impact of WWI and WWII, the oil and gas boom over the past 70-80 years (particularly offshore and in the marshes), and the greater penetration of national mass media/pop culture into American society.
The World Wars sent many rural young Cajuns, a large percentage of which had never left South Louisiana, overseas.
Between their wartime experiences and their exposure to American soldiers from other regions, the GIs coming back were more assimilated into mainstream American culture.
Likewise, the oil boom brought a lot of investment and integrated Acadiana into the US economy to an extent not seen before. Cajun culture in the larger towns and cities like Lafayette and Houma was diluted both by transplants in the oil industry as well as by Cajuns moving to pursue oil industry opportunities in Texas and further afield like Alaska or the Persian Gulf.
But I think the largest modern influence on the decline of Cajun French is probably the greater penetration Anglophone mass media (whether radio, TV, or social media) and the rise of pop/youth culture post WWII. There just wasn’t as much need to use French in everyday life and young Cajuns grew up bombarded by mainstream American culture. Heck, despite the fact that Louisiana’s diehard football culture transcends race, culture, and social-economic status, neither Saints games or LSU football games are broadcast in French (although both are available in Spanish these days).
Ironically, it may be local media that helps preserve Cajun French as a living entity as I understand there are several radio shows, podcasts, and public access TV shows dedicated to passing the language on to the next generation. That said, the remaining folks that primarily use French at home are almost always elderly.
There’s a ongoing renaissance of interest in Louisiana French, but even if the state pushes for earlier French education in public schools (I actually had it a couple times a week in 4th and 5th grade back in the late 90’s), I don’t see it ever regaining its mainstream status.
In my experiences in New Orleans and its suburbs, it seems that local educators see more value in pushing Spanish as a second language given the growing Hispanic community in Louisiana and the US as a whole. That also assumes that public schools can even fund language programs, which has been a real struggle for the state over the past few decades.