I think IE may be downloading the e-book but failing to open it with MS Reader and then (therefore) deleting it.
Try downloading
1632 by Eric Flint from the Baen Free library using Internet Explorer (select the unzipped MS Reader version). This took about a minute to download when I tried it. It was downloaded to a temporary file, but then MS Reader opened on 1632 and the .lit file ended up in My Documents\My Library. It is also now in the library view when ever I open MS Reader.
If this does not work for you, then there is something wrong with your MS Reader installation. If it does work, then try buying and downloading FictionWise's free test eBook
Origins of Wish You Well: A Short Essay. Clicking its "download ebook" link in "my bookshelf" should go through the same steps as for 1632 - the only difference is that (as AnemicOak says) there is a "text to speech has been disabled" popup once MS Reader opens. You can try this first if you like (skipping 1632), although I assume it will fail for you.
One final thing you could try is to follow the steps in Fictionwise's
Saving Microsoft Reader Files on your PC: this apparently avoids the need to actually open MS Reader. Fictionwise does not say so, but this seems to be the route to go if all you ever want to do with a LIT is download it for later format shifting.