I used to have a similar problem in IE7 in that I'd frequently get a popup asking me to download ActiveX (not just a runtime control like you're getting, but the application itself). It was annoying, plus after downloading the thing, I'd get the same message the next day on multiple websites LOL.
I wasted a lot of time searching for a fix, but in the end I think what resolved it was simply installing the Windows updates (I'm running Windows Vista and have my settings to notify me of updates and then let me choose when and which ones and I'm pretty lax about keeping up).
Or...it may have resolved itself when I obtained Silverlight (automatically installed when I downloaded Netflix Streaming)...or I suppose it could have been a combination of the two. My Programs Mgr. indicates I have Silverlight 3.0 and the install date corresponds to when I signed up for Netflix streaming.
Not sure if this will help your particular issue, but here's some discussion by users with a similar problem:
Re: IE 7 browser keeps asking me to download Silverlight 2 plugin but works in FireFox 3
I had the same problem. But later I figured out that my Silverlight application was built for Silverlight 2 Beta 2. The browser with Silverlight 2 Release installed can not run Beta 2 application and it would keep asking you for downloading a silverlight runtime. After I upgraded my development environment to Silverlight 2 and rebuilt my silverlight app, both IE 6/7 and Firefox worked fine. To double check if it is your silverlight runtime installation problem or not, you can go to www.microsoft.com/silverlight.
If your browser is able to view the silverlight components on the site, your installation is fine. Hope this helps.