I don't know whether BitPay is profiting.  

IIRC, when they started, they offered merchants a free entry-level plan, that allowed only some small volume.  Merchants who exceeded that volume would have to upgrade to a plan with a monthly fee.  But at some time they dropped all fees.

Even if they are processing 200 million USD/year of e-payments, and taking a percentage of that somehow, their revenue must be only 3-4 million USD/year.  Their payroll alone must be more than that.  

Didn't they lay off some staff recently? Anyone remembers how much they paid for the Bitcoin Bowl?

So perhaps they are still operating at a loss, burning their venture capital, hoping for a substantial traffic increase.  Which, again, would explain why they are not releasing any meaningful numbers.