Try and download the data sheet for the DS1232 from Maxim. Also called a reset controller this does the following for you:

1. Reset the controller when the power supply dips below a preselected level and hold it there till conditions stabilize.

2. Debounce your mechanical reset switch and produce a clean reset pulse that has a fixed pulse width.

3. Has a watch dog timer that can reset the MCU, if not tickled within three selectable time slots - 65mS / 250ms/2000 msec or so. For a start you just tie your MCU ALE to this tickling work and then maybe you can write code and connect via a port pin.

This behaviour of one-in-30 times OK start is clearly an issue to do with MCU start conditions ( in other words reset )

Raghu