As customers put the final touches on their Amazon Prime Day shopping list, some analysts and researchers are cautioning the e-commerce retailer’s biggest sale might not bring the same flood of customers and cash as it has in the past. It comes down to the usual suspects: inflation, competition and profitability. “This year, it’s a little less promotion, discounts are not as steep,” said Melissa Burdick, who works with sellers who advertise on the e-commerce platform through her software company Pacvue. Amazon could see a “more muted benefit” from Prime Day this year “given the challenging mac…