IMHO, the need in jQuery, ExtJS etc. will be eliminated as soon as XBL2, entire collection of CSS3 specifications, SVG and HTML5 all get available in an equal extent across all desktop/mobile web-browsers, which is not going to hapen within coming 5 years.
I look at ExtJS, and it appears to provide many of the RIA features that more bulky suites such as Flex provide, without the flash requirement.
To run Flex application you still need Flash player, which for example is not available on mobile devices
However, as Open-source initiatiatives such as jQuery-UI continue, will ExtJS simply die at some point?
Comparing ExtJS to jQuery-UI doesn't make good sense, since jQuery is primarily a cross-browser library to simplify operations on HTML documents and make web-pages nicer, while ExtJS is a true aplication framework that brings enhanced data-driven UI components to make applications easier.
Furthermore, since flash penetration only continues to increase, why put stock in a javascript library?
It doesn't really matter that Flash penetration "only continues to increase", since it is already available on 98% of desktop devices. Putting stock in a Javascript library makes sence, believe Google (who put most of its stock in DHTML)
will ExtJS simply die at some point?
Indeed it will, as at some point will die .Net, Java etc. It will not die in a foreseen future however and the need for this kind of Flesh-less solutions will only increase.
You may also want to take look into an alternative GUI framework Ample SDK, which will go Open-Source on 1st November this year. It enables tehnologies, such as SVG, XUL and more equally cross browser.