Both tubes?
Maybe the valves are a bit sticky and the pump is having a hard time overcoming the stiction+pressure? Try a quick drop/spray of lube inside the valve core and see if that helps.
Another thought is that the valve inside the pump itself is sticking somehow. I've never torn one of those pumps down but DO have a lot of experience servicing both Park and SKS pumps and have seen this before. With the Park pumps there were problems with the gauges themselves that created a similar situation. We had to swap the gauges out. With SKS I don't remember having this particular problem. Those pumps are serviceable and it was mostly about replacing seals and such.
I do love a good head scratcher, though.