No one asked, so I will...
What is your current setup? What heads, rockers, push rods, adjusters are utilized in this setup?
What type of driving? is this a race only setup? Does it spend any time at a idle when hot, like red light traffic? I have seen race cars do fine at the track, but the exact same setup on the street burns and smokes push rods. Lots and lots of factors can cause this. Lets say you have top notch stuff that is supplying plenty of oil up to the rocker gear. But the push-rods are about .100 too short. You have way to much adjuster hangout from the rocker arm. This can and will cause this.
A bad batch of adjusters can cause this, I recall one of the rocker companies, missing the heat treat on some of the parts causing adjusters to eat each other away.
With a stock setup, heads and lets say Iron Isky/Crane Ductile rockers, everything has to be in the ball park to work.. I have seen those rocker arms, not be drilled, or the oil hole be drilled in the wrong spot.
If your serious you can fix this on the cheap with a little sweat and a few skinned up knuckles. Run down or dig out a old stock set of valve covers. Cut the very top part, making a window so you can see whats going on. See where the oil is squirting etc. You could increase the size of this hole, banana groove the rockers for increased oiling..... Pull the cam and groove the 4th cam journal all the way around with a small .050 x .050 groove. This was always a trick the Hemi guys would do to oil the complicated valve gear on those. You could build a cheap spray bar oiling system (I did) out of 3/16 brake line feeding all the time straight from one of the oil galley plugs in the back of the block. Worked for my Jesel rocker arms, and 440-1 Indy heads. I was running 850 LBS open pressure turning 8Kand never once had a oiling issue to the valve train. And it was like $25 for the parts, of coarse most just buy the setup from Indy, which is in the $500 range last I checked. Think they wanted $350 to convert your supplied old covers to spray bar system.
Anyways, just some idea's to chew on. You really need to see whats going on, to find the problem and correct it. If you can get the system to oil good at idle with the engine/oil hot.. You wont need to worry again.