It is pretty irritating when that happens.
You could try this switch
Menu>
Preferences>
Configuration ManagerAttachment:
Selection_002.png [ 166.51 KiB | Viewed 4133 times ]
Other than that, I think placement on the desktop is the realm of the application.
For example, Sylpheed, the email client, re-opens in the last position and dimensions. Other applications might have a switch to turn off/on previous setting.
I'm not familiar with Thunderbird, but I think the developers might be pretty proud and want it to be 'front and center', every time it is launched, unless of course there is a switch inside Thunderbird that 'remembers' last placement.