jQueryUI's draggable/resizeable boxes make a number of extremely annoying and badly documented assumptions. They also don't play well with a lot of custom styling options. For example, I cannot even use the handles of the brush because jQuery is capturing my mouseup events.
However, in this case I believe you can solve the dragging problem by only letting the top bar be a "handle" in your jqueryUI setup.
Also you should probably bind the redraw to the resize event rather than the stop event, since the interaction is quite janky. Using the stop event callback, the interface feels laggy and if you shrink the box the graph sticks outside of it in a very glitchy way. Using resize will have it redraw as the user drags, which is more natural. If there is any performance concern, simple throttle the callback.
As for you actual question: the redraw function has [.3, .5] hard-coded as the brush extent, so that's what it will use. If you want to brush extent to persist, you need to store it somewhere outside of your redraw function and pass it in on redraw. See Mike's
article on making charts reuseable/"editable" for a very well-written guide to accomplish this.