Does it happen with a new oil filter? A bad oil filter with a faulty/intermittant bypass might do that.
Also, oil can crud up in older engines. There are some really thin oils that help break that stuff up, but you're only supposed to run them for a few hundred miles.
I remember reading an article about marvelous mystery oil once... It's a very very thin oil and if you dump a can of it into your oil, it thins it out and breaks up any clogged oil passages. You only run it for a few hundred miles, and then change your oil out normally. It's not something you want to run for a long time in demanding conditions, but it's a lot better off in the long run than slick 50 or those other treatments because the marvelous mystery oil cleans everything out, while the PTFE treatments deliberately add a buildup layer. Yea it's a slippery layer, but PTFE treatments can clog small oil passages over time.
The other thing it could be of course, is a bad oil temp or pressure sender. Those should be easy to replace and not terribly expensive either.