First, wouldn't it be better to start with a list of words instead of a regex?

my @words = qw( SA NV LTD CO LLC );
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So we'll need to build the regex programatically.

my ($re) = map qr/$_/i, join '|', map quotemeta, @words;
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Using Regexp::List can greatly speed up the process.

use Regexp::List qw( );
my $re = Regexp::List->new(modifiers => 'i')->list2re(@words);
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Now that we have the regex, let's avoid the fragility of 1 while s/// while properly removing spaces.

while (<>) {
   chomp;

   s/^ (?: $re \s+ )+//x;
   s/  (?: \s+ $re )+//xg;

   print("$_$/");
}
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Note: You were using capturing parens ((...)) when you only needed non-capturing parens ((?:...)). Removing the need to capture greatly improves the speed of regexs.

Update: Oops, it could still leave spaces. Fixed.
Update: Added Regexp::List method.