So what happened to the pump rifle?
All the negatives already mentioned without enough positives to make up for them. And that has been nothing new. I was just looking at my old Henry Stebbins book from 1958 (Rifles: A Modern Encyclopedia) and even back then, when stand hunting was not yet as popular and there was no black plastic or civilian ARs to be found, Remington's Model 760 was the only centerfire pump rifle on the market.
I suppose that another thing hurt the popularity of a pump deer rifle: maybe people didn't even know they existed. If they weren't seen on that many racks at pawn shops and other places that sold guns and not that many people (outside of PA) used them to hunt with, that couldn't help. They also didn't have any origin as, say, a police, military, or cowboy rifle, so they were never seen much in popular entertainment, if at all.
I did happen to be on the Remarms website and noticed that they were no longer showing the 7600 as a production model.