Rotary engine compression loss
The rotary engine loses compression as its internal seals wear, causing hard starts when hot, weak power, and stalling; Mazda’s extended 8-year/100,000-mile engine warranty has lapsed. Insist on a compression test by a rotary-familiar shop and ask the seller to restart the car fully warmed up. Many cars are on their second engine — paperwork for a newer engine is worth real money.
Ask for repair records covering this item. If it hasn't been addressed and the car is in or near the mileage window, price the $4,000–$8,000 repair into your offer — or make it the seller's problem.