Two things, you'll need to pick up a cheapy mechanical pressure gauge to verify the phenomenon is actually happening and not some sort of electrical gremlin.
The other is bad news. The oil pump pickup may be getting clogged. It's a fairly common problem. The o-ring that seals the oil pan from the factory tends to deteriorate and crumble into the pan. The oil pump pickup sucks this up and it the bigger chunks get sucked into the screen. At idle, there's enough flow through the pickup to provide oil pressure. As RPMs go up and the pump tries to provide more oil, it can't get it through the clogged pickup.
It sounds far-fetched but I've seen it first hand in my car (actually spun a bearing and ruined a rod and the crank) That's how I got it for free.
