Sorry, I can see why my example is confusing. Here's a slightly better one, more true to the production code:

#!/usr/bin/perl

use strict;
use warnings;
use Scalar::Util qw(looks_like_number);

my @times = (2, 4, 3, 1, 3.5, 2, 5);

select((select(STDOUT), $|=1)[0]);

TIME: for my $time_to_wait (@times) {
    print "Time to wait is: $time_to_wait\n";

    local $@;
    eval {
        # Skip even numbers.
        die '__NOT_FATAL__' if !($time_to_wait % 2);

        verify_number($time_to_wait);

        # Skip numbers less than 3.
        die '__NOT_FATAL__' if ($time_to_wait < 3);

        verify_time($time_to_wait);
        1;
    }
    or do {
        if($@ && $@ =~ /__NOT_FATAL__/) {
            next TIME;
        }

        print "Something went boom! ($@)\n";
    };

    print "Sleeping for $time_to_wait seconds ... ";
    sleep $time_to_wait;
    print "Done.\n";
}

exit 0;

sub verify_number {
    my ($arg) = @_;
    die "We died!" if !defined $arg;
    looks_like_number($arg) or die "We died!";
    return;
}

sub verify_time {
    my ($arg) = @_;
    die "We died!" if !defined $arg;
    # Floats not allowed.
    int($arg) == ($arg / 1) or die "We died!";
    return;
}
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Now imagine several more "verify" type calls within that same eval. Granted, it could be re-written to use a bunch more separate eval calls thus potentially allowing next calls outside/between them but in production those function calls are all very related and would die in similar ways. So I feel it comes down to what's more simple, cleaner? I think I might give the undermentioned Syntax::Keyword::Try package a try (swidt) since it does seem to support exiting via "next" calls.

Now imagine several more "verify" type calls within that same eval.

Yeah, I figured it was something like that. Personally I still wouldn't use that "eval/die with a fixed string" pattern, and instead maybe wrap each call in an eval, or to make it look a little nicer, perhaps Try::Tiny. Of course, this being Perl, other ways come to mind :-) Say you've got a bunch of verify_* functions that you can't change and whose errors are fatal, but you want nonfatal versions of them:

use warnings;
use strict;

# UUT
use Scalar::Util qw/looks_like_number/;
sub verify_number {
    my ($arg) = @_;
    die "not a number" if !defined $arg;
    looks_like_number($arg) or die "not a number";
    return;
}

# wrap the funcs
my @funcs = qw/ verify_number /;
for my $f (@funcs) {
    my $orig = \&{$f};
    my $wrapped = sub { eval { $orig->(@_); 1 } };
    { no strict 'refs'; *{$f.'_nf'} = $wrapped }
}

use Test::More tests => 4;

# helper
sub exception (&)
    { eval { shift->(); 1 } ? undef : ($@ || die "\$@ was false") }

ok  !exception { verify_number("3.14") };
like exception { verify_number("foo")  }, qr/\bnot a number\b/i;

ok  verify_number_nf("3.14");
ok !verify_number_nf("foo");
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Of course you don't need to install the wrapped versions into the symbol table, a hash would work fine too.