Although some HTML apps have this problem too, Flash is invariably laggy.
Flash doesn't work well on Linux, and many of the people in my world run Linux desktops. (And some won't run proprietary software on principle.)
The UI of Flash apps is always some homegrown awfulness that tries hard but is never as intuitive or responsive as native UI, and not even as good as web browser controls.
With Flash apps, printing usually doesn't work as you expect.
You can't save the page.
Flash apps don't really exist on the web. Even if you give each Flash app its own URL, that just means you re-download the same framework over and over again and then load the data.
It is cumbersome (for instance) to bookmark, or bookmark a particular view, or to link directly to other content, or to have a task expand to show an iframe of other content on the web. Some advanced HTML apps have similar difficulties in practice, but Flash apps have these issues in principle.
None of my existing web browser plugins work well with Flash content. For example, some people have spellcheck built into their browsers; now they can't use that when entering data. Even something as simple as cut and paste sometimes doesn't work quite right.
Flash works great on Windows, and unlike HTML5 it works in IE6 which is what your market is still probably running on their corporate network.
No flaming intended, btw. I have a PC, Mac and a Linux netbook running right now on my desk. Chrome tabs die all the time in Linux when running Flash and my Mac beachballs sometimes running large swfs. My PC browsers (FF and IE) have never puked once over Flash.
Interface lag when I drag things means I'm never going to use it - it can't compete against the many good desktop apps out there for me (plus, being flash means it wont work on my smartphone and iPad, which would have been a case for giving up on desktop apps) HTML/JS apps can have a ton of lag in sending things to the server before it gets frustrating, but dragging something and having it not move until a little bit later is too frustrating for me to use.
Take that with a grain of salt, though, I'm one of the people who get's extremely frustrated when having to use monitors not at their native resolutions (curse you DVDs on HD screens!)