How about sleeping until the next polling interval (based on when you started looping) instead of a hardcoded delay? This will account for however long your processing takes (even if the amount of time it takes to process changes). It can be "off" by a fraction of a second, but should correct itself so the drift does not accumulate.

my $t0=time();
while(1){
  # do processing 
  # ..

  # sleep till next polling interval.
  sleep 60-(time()-$t0)%60;
}
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Use this concept with Time::HiRes for greater accuracy.