When this happens to me it is because EQ misidentifies the width of the window because of the page arrow buttons. If you hide those it's length will only be remembered by the length of the hotbuttons themselves and it shouldn't reset. Also, camp out fully and click quit instead of /q to make sure settings are saved.
Is is possible to mod the hotkeys xml file to place the page arrow buttons at the bottom of the window where the buttons would then set the width of the window?
Yes you can move the arrows to bottom but won't necessarily fix your issue .best way is set everything the way you want then zone ..this forces eq to save your settings should work then.if it doesn't I would recommend clearing all window settings from your character INI setting your windows then zone to force a save.