What part of the cycle has to be accurate?
The 30-seconds, the 29-seconds, the one second, the periods, the intervals, or seconds per day? Have you ever noticed how accurate those cheap, battery-operated, wall or desk clocks are? When was the last time you had to reset one that was off...except twice a year. They are a good, "quartz crystal", 1-second clock source:
<A href='http://www.josepino.com/circuits/index?one_second_timebase.jpc' Target=_Blank>External Web Link</a>
You would need to add a voltage dropping circuit to replace the 1.5v battery, and maybe a drive transisor/FET to bring the clock to an input logic level. But, it should be as accurate as the time for the Picaxe to count input pulses and do what ever you need to output.
Ken