This won't be a popular opinion, but I would have to say that the strongest Double Action .44 Magnum Revolver in current production is the Taurus Raging Bull 444.
The Raging Bull was designed for .454 Casull, and the Model 444 reflects that, as it is a .454 Casull Revolver chambered in .44 Magnum.
The gun is an absolute beast, weighing in at 53oz with front and rear cylinder latches to insure that it stays locked up tight while firing even the hottests of .454 Casull loads, and based on what I've read, the Raging Bull holds up pretty much indefinitely to .454 Casull, so I imagine that it would basically be indestructible firing .44 Magnum.
Last but not least, the Raging Bull, like most of Taurus' Magnum Revolvers, has significantly higher QC than Taurus' usual bargain-priced handguns, and the price point reflects this, as the Raging Bull costs about as much as a Ruger or Smith & Wesson does. The MSRP on the Raging Bull 444 is $899, typical gunstore prices are about $100 to $125 less. Some would say that's too expensive for a Taurus, and for the money they'd rather buy a Ruger or Smith & Wesson, which is understandable. I myself would sooner buy a Smith & Wesson at that price, but the question was in regards to the strongest .44 Magnum Revolver on the market, and in my opinion, when it comes to DA Revolvers, the Taurus Raging Bull is just that.