When you save a modified picture, the 3 timestamps are modified to current date:time.
there is no option (checkbox) in tools/options for asking to keep original date:time, except for rotation .
There is a workaround: change date using exif date after saving
In Windows versions ( I use 1.97 on Ubuntu_10.04LTS/Wine and on Windows-XP-sp3 ),
the option "Conserver la date/heure lors de la sauvegarde" = "keep date/time when saving" (last checked checkbox) is effective on any write (and I think it's the way it should be) :