You definitely have an air leak somewhere. You should be able to run wide open or anywhere in between without losing prime. You could pressurize the pump and lines with air, CO2 or even water to check for leaks. With air or gas, you could spray everything down with soapy water and look for bubbles. It only takes a tiny leak to cause a problem. I would only dismantle and start over as a last resort. Hose clamps can sometimes be the source of leaks. This is usually due to the hoses softening up when exposed to heat. Check those first.