It's hard to know without seeing your screen layout, or a before and after screenshot. Are you using Paratext 9.3? Windows programs often don't like staying put, especially if they're tiny, and especially if switching between a laptop screen and a monitor.
If you are using just a single pane, you could consider opening it as a floating window. That floating window might be more likely to stay where you want it.
As a last resort you could use a program that lets you define specific regions where you want a window to live. I have used Microsoft Power Toys (Fancy Zones) to create custom areas that let me quickly snap windows to that spot. I just hold shift and the zones that I have created appear and I can drag my window to that spot.