You read from ADDRESS in a loop, but it is opened for writing.
So the loop ends after the first round and the program exits.

I think you should use something else to control that loop.

Change the while (<ADDRESS>) { to while (1) { and add something like:

print 'Enter another address?';
my $answer = <>;
last if $answer !~ /[yY]/;
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at the end of the loop.