Battery problem?

Two weeks ago I went to start my '78 Granada and the battery was completely dead. I only drive this car once a week now but I used to drive it every day to work. I checked immediately to see if I left
anything on. Nothing was left on. I didn't leave the lights on, the hood, trunk, and glove box were all closed so their lights were off. The only things that always connected to the battery are the digital clock and the am/fm cassette radio. I charged the battery and installed it on my other car. The car started every day over a week period. I reinstalled the battery on the Granada, which is left outside. After driving the car about 80 miles or so, I parked in front of my house and disconnected one battery cable. I wanted to elimintate the cold causing the battery to discharge. After 1 week, I reconnected the battery cable and the car started immediately. I drove another 80 miles, returned home, and left both battery cables connected. Last Thursday, the battery was again dead. The only thing I suspect is that this 6 year old battery can't source the very small current to turn the digital clock and keep the time and channels memory of the am/fm cassette radio 24 hours a day for a few days. I can disconnect the wires for the clock and radio.
The Granada is charging the battery. I connected a shunt between the alternator and the wire that goes to it and the meter shows the charge current. I also put a voltmeter across the battery posts and when the engine is running I read 15 volts. With the engine off I read 12 volts. Does it sound like it is time to replace the battery?
Thank you
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fully charge the battery, and do a load test. that will tell you if the battery is good or not

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In hot weather like we have in Vegas, batteries can die overnight. Works fine one day, next day you go out and its dead as a doornail. No amount of recharging or anything else will bring them back. It's been really hot in lots of the country and when you add six years into the mix it is possible that your battery is beyond its useful life. If you have a dead diode in your alternator it goes like this. You charge it, it works fine all day, you go places and it starts fine, but when you leave it overnight its dead the next morning. You charge, battery takes a charge, and you leave it overnight and its dead again. My personal experience on both problems, of course it always happens in 105 degree weather.
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Did you connect an ammeter between the bat and alt out?
Maybe a high resistance diode short.
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