Also check that the alternator is actually charging the battery in the car by taking a battery voltage reading with the engine off then another with the engine running. The 2nd reading should be higher than the 1st and climbing steadily. And also check that the alternator is secure to the engine as this provides the ground for the charging circuit and make sure that the engine / gearbox earth strap is secure and the contacts are clean and bright.
And one last thing is – how old is the battery? – As even good quality ones need replacing every 5 years and faulty battery just won’t hold a charge