iTunes cuts out mid download with err = - 3150

Using PC, latest version of iTunes, it lets me browse items to my heart's content, processes purchases happily taking my money and telling me I can have the album files... Oh wait! No, you can't - "we" can't make a secure connection! Which I find odd - not to mention mildly aggravating - because there was definitely a connection when I searched for the album, there was definitely a connection when I selected the album, there was definitely a connection when iTunes took my money, and there was very definitely a connection for the first 6 tracks. But that connection seems to have completely broken for the rest of the album.

I can still somehow browse for other albums on iTunes (as well as browse the web) so the connection is there... it just seems to vanish when I want to download the rest of the album I paid for! Tell me how this is better than just pirating the album, and giving a donation to the artist? Because Apple takes my money but seems to taking great delight in preventing me from having the complete album.

Note: I signed in, and created this question while iTunes told me there was no connection.