Q: I have replaced the battery and alternator and the charging system light keeps popping on and then the car dies after a day or two

I recently was driving my car and all of the indicator lights came on and when I would push on the gas I would slowly move then jerk to get to a faster speed and it became difficult to steer. Bought a new battery, and replaced the alternator. Every once in a while the charging system light (the one that looks like a battery) will come on. Sometimes it stays on for the whole day, and sometimes it says on for a few minutes going on and off during those 20-30 minutes. Then after a few days the car will die. Sometimes after it sits it will start again and last for a day or so, but continue on the same cycle mentioned above. I had the battery and alternator tested and they are fine. Talked to a service tech at a mazda dealer on the phone and he said it could be corrosion in the cables connected to the battery. Any idea if this is the problem and if not, any other ideas? Thanks

My car has 151000 miles.
My car has an automatic transmission.