'88 Volvo 240 battery runs down and then won't start

'88 Volvo 240 DL wagon, I've had the ground replaced a year ago, have now had the battery replaced twice within the last month, the mechanics say I need a new alternator, they put in a new alternator and the same problem persists three days after -- I drive the car for 45 mins. To an hour, it's driving fine, when it's time to re-start it, it struggles to start, sounds like a low battery. Each successive time restarting it, the battery has less and less power, it'll take a jump just fine, but once it's time to turn off and restart, same thing. All of this started during a frigid cold snap two months ago, the mechanics said the battery was weak, that's when I got a second new battery, it runs for two weeks, then problems persist, the mechanics say the voltage swings so it must be the alternator, and 4-5 hrs of driving time and now the car won't start!