Check the terminals at the battery - they must be free of corrosion and tight on the battery posts. If this looks good, inspect the cables for swelling indicating internal corrosion. This has happened to others.
Check the voltage output at the alternator.
volvolugnut

Hi Everyone! Recently, my son's 2004 XC70 started exhibiting a weak battery. When I put a multimeter on the battery leads with the engine running, it was showing less than 12 volts. Last week, we replaced the voltage regulator with a new Bosch unit because the old brushes were a bit worn down. The ...