is it possible for a hospitality operation to be operating at a profit durany any given month but to simultaneously have insufficient cash flow during that same month

Yes

Explanation:

Cash flow is defined as the available cash for business operation as a result of the difference between the cash available at the beginning of a period and the cash available at the end of that period,

One major factor responsible for an insufficient cash flow is the bad timing of income and expenses. Imagine your bills are due and overdue customers invoices are not yet paid. It may also be that a lot is invested in the inventory while a little income is earned.

When more is being spent on investment compared to what is coming in, it can also lead to poor cash flow.

As an hospitality also engages in activities that could impact cash flow as mentioned above, it is possible it operates at profit and still have an insufficient cash flow.