Is it possible that a profitable company may be in a situation of default? Explain

Yes,

This could happen if the cash flow is not properly managed. The company might be profitable but the stakeholders or the partners shall be withdrawing excessive money. As this is not reflected as an expense and only capital withdrawal/ loans to partners/ shareholders.

Another case is where the company invests heavily on capital expenditure like a machinearies and equipments.

All these cash flows will have a pressure on the dues which eventually turnout to be a default.

In short, if the cash flow is not properly managed, irrespective of whether the business is on profit or not, it may be in a situation of default