Hi Siddharth,

As mentioned :
1. you are waiting for the RTC interrupt to update the time through software.
2. clock freezes; and after manual reset, it starts counting the time when the clock had freezed.

When the clock freezed, did the other functions of your product also freezed, example: Keyboard, Display, other activities of your product apart from RTC ?

Add up the above 2 points, and it most probably means, that the Oscillator has stopped, hence the "interrupt" is not generated, and hence your RTC freezed.
After manual reset, the oscillator is again started by writing the control word, and everything works as "a Priest on Sunday" (its a quote from "BackToTheFuture-3").

Check your software again, are you un-intentionally reading/writing on IIC bus ?
Or else the RTC chip has gone bad.
It may be because of Power Glithces/Noise, check for decoupling capacitors, and the power supply circuits again.

Keep Noise generating devices and circuits away, as far as possible, atleast to verify that the problem is due to Noise or not?