OK, so now we go onto the next step; add the column for the month to the query and test it again.
Mth: [Forms]![Production_CenterDetails_Main_Form]![Text37]
So the SQL should now be:
SELECT DISTINCT CenterCode, StudentID, CourseID, [Forms]![Production_CenterDetails_Main_Form]![Text37] AS Mth
FROM tblStudents, tblCourse
WHERE CenterCode=Forms![Production_CenterDetails_Main_Form]![CenterCode];
If that still works then convert the query to an Append Query so the SQL should be:
INSERT INTO tblStudentProgress (CenterCode, StudentID, CourseID, GradeMonth)
SELECT DISTINCT CenterCode, StudentID, CourseID, [Forms]![Production_CenterDetails_Main_Form]![Text37] AS Mth
FROM tblStudents, tblCourse
WHERE CenterCode=Forms![Production_CenterDetails_Main_Form]![CenterCode];
Then empty tblStudentProgress and try the button again.