Gangabass,
First, I too would probably subclass WWW::Mechanize so that you don't need to keep sprinkling this code all over the place - something like:

sub my_get {
    my ($self) = shift(@_);
    my $result;
    eval { $result = $self->get(@_); };
    # ... if $@
    return $result;
}
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Second, I would probably avoid the evil goto - something like:

my $success;
while (! $success) {
    eval { $mech->get(@_); };
    if (! $@) {
        $success = 1;
    }
    else {
        sleep $CONFIG{DELAY};
    }
}
[download]

Third, I would consider that you have introduced an infinite loop and would probably re-write it to include a $CONFIG{MAX_RETRY}. The code above is not intended to be copy/paste but give you an idea of how it might be accomplished - you will need to fill in the blanks.

If your real problem is that you have never sub-classed before at all then you should probably make that clear. After reading your question again, I am not sure if you just don't know how to subclass in general or how to write the wrapper to do what you want.