Test the alternator output with a multimeter set to 20v DC across the battery terminals.
1. Engine off
2. Engine running, no electrical load
3. Everything switched on -- headlights, rear screen demister, etc.
Get the battery drop tested (lots of places will do this for free).
If both check out OK, either a big electrical drain with ignition off (aftermarket stereos are often culprits as are boot light switches) or dodgy connection to battery, earths, or starter motor.