I would just say, in my experience, that when it's a large-scale company paying late, it's not been cash-flow issues, but their feeling that they can dictate their own payment terms because of their size.

I always consider not just what the money is to me, but what that sum of money is to the client. Do they understand that, although it's a small invoice to them, it's an important one to you?

EDIT: I should say, I'm not calling your client a liar! I'm just saying, you know, their idea of no money might be different to yours. I'd debate if it's really that they can't pay you, or that they'd rather not.

I had a difficult time with a client recently, but the only solution that stands is to be in contact regularly, explain to them the importance of it, and literally ask whoever you deal with (accounts, or the contact) to help you get it paid.

For future reference it can be worth doing a credit-check before you get involved, although it's another expense. You can also elect to charge interest on late payments, which gets them moving!