66 Valiant Starting Aggravation

I have a 66 Valiant that starts right up 95% of the time, the rest of the time it acts like the battery is dead. The battery is about four years old, but when it is working acts like it has plenty of power. The Starter has just been replaced, and also kicks with plenty of power. Drove it to church yesterday, and it fired right up, cruised around and it did great, then this morning it acts like its dead again. Last week, started up, to go to work, started up after work. Got home cut it off and in 30 minutes tried to Crank it and it would barely turn over. I jumped started it and it took right off. I drove it ten miles and cut if off, it would not start. Left it one the charger all night and it started again.

Since it cranks most of the time with plenty of power, is this a Battery issue? The car is a 3 on the tree with a 225 slant 6. Thanks!