Engine Idles Rough or Stalls When Cold on Mazda MX-5 Miata

The engine may idle roughly or stall when it's cold because the oil pump pressure relief plunger is sticking. Failure is usually due to wear and it causes excessive oil pressure to pump up the hydraulic valve lifters keeping the valves from closing completely, which results in a loss of compression. The oil pump will need to be replaced in this case.