What kind of transmission do you have? I had this same issue when I first got my Ram. Didn't find it until I did the clutch. Turns out, the truck had a crack in the flywheel. New flywheel in and it never happened again.

Could also be spring wrap in the rear leaves. Do you have blocks under the rear leaves?

 

It's got the 46re. I think it's a combination of spring wrap, the snap ring in the t case being broken and bad fluid in the rear end.

I changed the fluid in the diff and it's a lot happier, problem is like 90% gone. I'm gonna go after the snap ring next but I can't break the bolts loose to the driveshaft yoke at the axle so I have to take it to my buddy's shop when we both have more time.
Then I can put in my t case saver.

After that I'm gonna change the fluid in the trans and adjust the band's.

Then eventually I'm gonna get a shackle flip for the rear so I can get rid of the blocks.