Need help analyzing broken/missing reverse zone

Hello,

I'm having trouble determining why my reverse zones aren't "working".
My name server is BIND 8.3.7-REL and is listening on 5 static IPs.

Also, I'd like to keep the actual names/IP numbers hidden from public
view in these posts and am not sure the accepted technique for doing
so.

In a nutshell, the reverse works when I query the name server from the
localhost (using dig -x). When I issue the same dig command from a
remote machine, I do not get an ANSWER: In fact, the SOA in the
AUTHORITY SECTION: is the netblock's ISP. Does the ISP have to do
something to make my name server authoritative for a reverse zone
lookup?

I've searched the newsgroup and googled, but apparantly I cannot phrase
my question adequately to find useful posts. My copy of O'Reilly's
BIND book isn't helping much either.

Thanks for the help,
Doug