After much trial and error, I was able to identify the following fix:
- Make sure that the video you want to render as an FLV is located on your hard drive.
- From the Start menu select Run.
- In the Open field, type "msconfig" then click OK.
- From the General tab, select "Diagnostic Startup" then click the "OK" button.
- At the prompt, select "Restart".
- Once your PC has restarted, run AME and encode the video you saved on your hard drive.
- Repeat steps 1-5, except select "Normal Startup" instead of "Diagnostic Startup".
As far as I can tell, this fix seems to work when using a PC where your Windows profile is stored on a network share.