One of my businesses can easily pay the wages of an employee for the time they are needed, but being highly seasonal work, it would not pay for an employee year round. Or to put it another way: On a per hour of work basis, it makes a programmers salaries look like chump-change, but amortized out to a yearly income it's not enough to sustain a living.
Sure - that's the same as "my business is profitable, but can't afford to hire another employee yet", only it's a fractional employee that you can't afford to hire.
Is that profitable?