Plato stores some of its data in the registry and some in Plato.ini (or Plato3.ini depending on which operating system you have and where Plato.exe is located).
The location and size of the main window is stored in Plato.ini under [OpenFiles] and M= ....
Assuming that you are using Windows 7 and that Plato.exe is located in C:\Program Files (x86)\Silverfrost\FTN95 and you are not running Plato 'As administrator' then you should find Plato.ini in %APPDATA%\Silverfrost\FTN95. (Blame Microsoft for this.)
If the position and size are not being restored then something is going wrong with the redirection or the access rights to Plato.ini. If you can 'Run as administrator' and the problem goes away then this will give you a clue.
One solution is to move Plato (together with its data files) away from the protected 'Program Files' folder.
The data files for Plato are Plato.ini, ClipLib.ini, UserClipLib.ini and English.lex.