Path not filling correctly

I have some paths that have been imported via SVG from Illustrator, and as I was splitting them up, some would fill and some wouldn't. Even after removing extra points and ensuring there wasn't any redundancy or open ends, the path still won't fill.

Even weirder, if I translate certain points enough, it will fill.

Unfilled:

Filled after severe deformation of an anchor:

What gives? I fixed the G earlier but now the T (consisting of only straight lines) won't fill. I have one other letter with many more points and I'd rather understand why it's doing this before spending more time fiddling with it before it works.

• Could you upload a .blend file where this is happening? It's hard to say what could be the cause without looking at it closer. – gandalf3 Apr 17 '14 at 2:50
• @gandalf3 <Surely>. In the blend file I included the other letter I mentioned as well. I haven't verified the U yet but I'm pretty sure it's closed (it was closed in AI so unless it imported weird it should be) – Qix - MONICA WAS MISTREATED Apr 17 '14 at 16:07

The object has a scale of over 40,000. If you apply the scale (CtrlA> Scale) everything will work correctly: