Car's battery isn't keeping it's charge with a brand new Alternator/Battery

Alright guys, so my car has been having some battery issues. I first replaced the battery with no luck, and so then I pulled out the Alternator and took it to my local Autozone and it failed so I then purchased one of there new ones. The car was doing awesome for the last couple of days but then the battery sign came on on my dashboard, and then the car just died on me. I checked all of the connections, they were tight and snug. The belt on the alternator wasn't to tight ( thinking that it was straining it). Everything on the outside looks like it's doing fine, but what worries me is it's most likely somewhere on the inside. Thank you for taking the time to read this, I can take any advice I can get!