I think that you are using your clock (seconds) as a reference to generate pulses at a given rate per minute. So, to mantain the reference precision , you have to derive the output from it. One way is using the reference to clock a state machine.(divider).
May be you could use some analog methods, for example: clock signal could control a current source, which is applied to a capacitor, this way voltage capacitor increases linearly, then with a comparator you can discharge the capacitor a generate the minute rate pulse.
But I am a digital FAN, with a uC you get more precision.