Instead of "sleep 45" you can sleep until the start of the next minute with Time::HiRes:

use Time::HiRes qw{ time sleep };
...
my $now = time;
sleep 60 - ( $now - 60 * int ( $now / 60 ) );
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You might need to subtract a fraction of a second from the sleep interval if the log entries tend to end in :01 rather than :00.