I had them checked but it didn't seem to work. Actually looking again it works OK when I have the application on my first (main) monitor but not when I have it on my secondary monitor.
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Save on exit in the Window Size group of Edit > Settings > Console will save the size on exit (and restore it on the next start).
Save on exit in the Position group of Edit > Settings > Appearance will save the position on exit (it implies the Intial position check).
I had them checked but it didn't seem to work. Actually looking again it works OK when I have the application on my first (main) monitor but not when I have it on my secondary monitor.
Does it work for you if you uncheck Snap to desktop edges in Appearance section?
If so, I believe there is a bug report about Snap to edges.