Automatically saving any record changes directly to the database would be a helpful feature and it would simplify the data entry process.
Changes could be saved either directly after each field change or after moving to another record.
Saving after each field change could slow down data entry because the round trip from making the field change to updating the UI would be much more complex. This is because each field change could cause cascading changes in other fields due to table triggers or other database interactions.
NOTE: Please vote on this Feature Request if it interests you.