Yes, Diamonds has an autosave-function. This function can be found in the menu Options > Preferences > Tab page File. Check the option Save file automatically and indicate the frequency. Keep in mind that setting the frequency very high (like every 5 minutes), might interrupt your workflow as you will be able to use Diamonds during the saving process. Therefore it is recommended to use a lower frequency. The larger the model, the longeer the saving procedure will take.
Note: the use of the option Save file automatically like described above is optional. The use of the option Save a temporarly back-up file automatically is recommended and is default active. This function creates a *.bs!-file containing a back-up of the geometry and loads. This *.bs!-file can be used to recover a corrupt *.bsf-model.