I don't think Adobe abandoned Flash -- they saw the writing on the wall due to declining support. It started with Apple coming out and officially stating[1] why they thought Adobe was bad for their devices -- even for the desktop OSX.
And since Apple devices have such a large market share, many web sites realized they needed to switch to HTML5 to support this market share.
I also think Apple's public rejection of Flash affected its reputation, and Flash was seen as an outcast by some. It became "cool" to switch to HTML5.
It was a snowball effect that resulted in their ultimate demise.
That's how I observed it anyway over the past few years.