Car shuts off after jump start?

I have been having car issues for almost a year and half. I don’t drive often therefore the battery died frequently and I had to call AAA for jump start and they also replaced the battery; worked fine for couple of months
The same issue reappeared, and it was recommended that the alternator need to be replaced. It worked for few weeks, and I was back to the same battery issue. I bought a Costco battery that worked fine for a week and same issue appeared. Now the car can jump start run for about 5-10 mins and then its lights on the front panel goes off and then it’s completely dead. Same cycle dead jumpstart runs for 5 minutes then completely dead.