Actionscript was closely tied to Flash and other Adobe products, so when they went out of fashion Actionscript didn't stand much of a chance.

I suspect the big problem with Flash was its business model. Adobe charged Flash developers for the dev tools but gave away the runtime environment to users for free. So every time a new phone, console etc came out they had to do extra work for no extra revenue.

Although it would have fallen eventually given the way HTML has grown in capabilities.