Peter:
This time I try to help you more specifically. I downloaded the data sheet for the RS5C72A RTC chip. I now understand more what your issue is.

The RTC in the periodic interrupt mode for one interrupt per minute will operate its output in what RICHO calls LEVEL MODE. If you look closely at the data sheet on the top of page 18 you will notice that in the RICHO level mode it is necessary for the software to send a command to the RTC chip to clear the CTFG in the Control Register #2 to a Zero level. This will cause the interrupt output to go back off (high). It is not clear to me from looking at the data sheet if you must then write a One back to the CTFG bit in order to setup the periodic output for the next minute. You will have to experiment to determine if this is needed or not. It may be that you just need to write the zero to CTFG once per minute interrupt.

The choice of how to handle the interrupt on the 8051 is a seperate choice from how the RTC works. The interrupt on the 8051 can be configured as LOW LEVEL active (which means continute to interrupt as long as the input stays low) or EDGE MODE (which means interrupt on falling edge of the input and while it stays low but just once). You can pick either mode in the 8051.

Does this help you understand now?
Mike Karas