Misbehaving woff file - one font loads, the other doesn't

I'm building a website that uses two purchased fonts, both .woff. One loads correctly, the other doesn't, and the console logs an error 'File not found'. A quick Google suggested this might be the solution: Why is @font-face throwing a 404 error on woff files? However, if this was the case, surely the other woff file wouldn't load either? What on earth is going on?