I was surprised at just how bad the Milanese Loop band was at staying fastened, and couldn't explain why some people were having problems and others weren't.
Reversing the band solved the problem for me.
The band is reversible, in the sense that the side that is fixed and the side that is looped can be swapped. If you're having trouble with slippage, try swapping the two sides using these instructions

This significantly reduced slippage for me and made the band much more pleasant to use. I almost never think about slippage anymore.
The reason this works (I believe) is because of the way our forearms are constructed. When we rotate our wrist, the ulna on the bottom stays relatively fixed and the radius rotates around it, causing more motion on the top side of our wrist (by our thumbs) than on the bottom. Moving the fixed band to the motion side decreases the tension on the loop, reducing the chance of slippage.