Hello Coolflex!
From here it sounds like the battery not the ignition - and yes, the alternator could be failing to keep it charged. The clicking is the sound of the starter motor solenoid failing to stay engaged when the motor draws all remaining battery current (solenoid disengages/starter motor stops/solenoid engages, and so on).
Give the battery an overnight charge on a good battery charger and if that brings everything right again, check the alternator brushes. The brush holder usually unscrews from the end of the alternator body. Brushes should be sticking out at least 6mm. Usually one is worn more than the other.
If the battery doesn't come right after an overnight charge, replace it. They do fail sometimes for no apparent reason.
good luck!
-Alex