You need a sliding buffer--a supersearch for that term will turn up various implementations.

Here's a simple one implemented using an array of lines:

#! perl -slw
use strict;

my @lines;
my %seen;
while( <DATA> ) {
    push @lines, $_;
    my $buf = join '', @lines;
    if( $buf =~ /(.{30}these\s+are\s+my\s+keywords.{30})/sm ) {
        print "'$1'" unless $seen{ $1 };
        ++$seen{ $1 };
    }
    shift @lines if @lines > 5;
}

__END__
Here is my text file
I want to save a bunch of
charcaters before the keywords
for example the keywords might be
the phrase: these are my keywords
I want to save a bunch of characters
after the keywords too so I have
context

The keywords may appear multiple
times in any given file and may
span across lines like so: these are
my keywords.  This is one reason
I was using slurp instead of reading
in line by line
[download]

Which produces:

C:\test>junk
'eywords might be
 the phrase: these are my keywords
 I want to save a bunch of ch'
'y
 span across lines like so: these are
 my keywords.  This is one reason
 I was u'
[download]

You would probably want to make the context at either end optional so you don't miss matches at the start or end of the file where there may not be enough context to match.