I also use the PCF8583 but have not faced a problem like what you mentioned. The data sheet warns about the way to load the clock registers :

"It is recommended to set the stop counting flag of the
control/status register before loading the actual time into
the counters. Loading of illegal states may lead to a
temporary clock malfunction."

Just check if you are violating this guideline. Also I am not sure what you mean by "solder this IC again " . Do you mean heating it ?

I also do hope that you have pulled up the SDA and SCK lines properly. And pay attention to the maximum ratings for supply volts and such stuff. Most such odd behaviours can be traced to poor application of the product...

Raghu