srj0408:
I hope that if it EOSC , the bit which you told is responsible for Oscillator ON/OFF mode, is 1 will not damage the Oscillator or DS1337.
It won't harm the DS1337 nor the oscillator if you set it to 1.
Earlier it was 1, but now i changed it to 0.
Question is: How did it get '1' in the first place?
Try reading it out in runtime, maybe some part of your code is constantly setting it to 1.