You may be getting confused on the difference between profit ($) and profitability (%).
If profits are stagnant then either a) revenue and costs haven't changed or b) revenues and costs changed by the same amount (e.g. $100 rev, $80 cost, $20 profit can change to $150 revenue, $130 cost, $20 profit). BUT, in that case profitability changed from $20/100 = 20% to $20/150 = 13.3%. So you're right, profits can be stagnating when revenue and costs decrease by the same amount, and that is something that you would want to test for.
If profitability is stagnant then revenues and costs must have increased by the same proportion (e.g. using the example above, going to $150 rev, $120 costs, $30 profit). The profit is higher but the level of profitability is the same, still 20%. It can be confusing because sometimes people say profit margin and you don't know what they are referring to, so in a case setting you should definitely clarify if they mean $ or %.