Thanks again for the response.
I wonder if it's possible that there's some kind of interference between the activity of Internet Download Manager within IE and the way HTML EXE handles Flash files.
I'm afraid disabling firewall software on the clients' computers doesn't solve this issue. To find out what is causing the problem, I think we should focus on the different ways that publications of programs such as Autoplay Media Studio and HTML EXE handle web object (IE) execution. The former literally doesn't offer any kind of setting for this purpose. Unfortunately I don't have enough knowledge to investigate this.
In any case, I updated a popular publication that had this problem and checked "Disable HTTPNegociateProtocol" to see if this solves the problem. I'm going to have to wait a week or two for client feedback.
Thanks for the tip about ExeOutput and Flash player. I had completely overlooked this fact because I thought the exe file already included flash runtime. I actually hope you guys can find a way to include flash runtime in HTML EXE publications!
I'll keep you posted on the results of our little experiment here.