Trying to d/l from main installer page, http://donate.libreoffice.org/home/dl/win-x86/4.1.2/en-US/LibreOffice_4.1.2_Win_x86.msiand I get “The connection to the server was reset while the page was loading.”
I’ve tried this on two separate computers, same problem occurs.
Are there any mirror sites I can use?
Yes, there are plenty 
Look at the nearest mirror list below the sentence
“Found X mirrors which handle this country (XX):”
Alternatively you can choose yourself from
http://download.documentfoundation.org/mirmon/allmirrors.html
Neither one of those links work for me either. Unless there is something going on with the main documentfoundation.org site, I guess it must be some glitch with my computers or internet connection (although it’s working for everything else).
I’ll wait a day and see if the problem sorts itself out.
You can try downloading from three party site like FileHippo: http://www.filehippo.com/download_libreoffice/16103/