*** Mmmmm, their IT department might ignore they have one. Example if it's a small company with hosted e-mails service. They will tell you they don't block anything, but their provider / hosted-service provider (call them what you want) will for them.
You appear in a few blacklists, check here:
http://www.dnsbl.info/dnsbl-database-check.php
I used your 2 IPs:
dotcad.in A 202.137.237.27
dotcad.in A 202.137.236.10
This one was ok:
dotcad.co.in A 74.53.251.150
If their provider uses this lists, you might be blocked.
Where are you e-mail sent from? from one of those 3 IPs ? or from your something else ? your MX for dotcad.in is some third-party company I guess (mail.rediffmailpro.com) and for dotcad.co.in, it seems to be a fourth IP/host (74.55.15.98)
Some e-mails servers don't like mails sent from @one.domain relayed from an host whose FQDN is not "one.domain"
*** Ask your vendor to check their logs and look for incoming connections from the IP you are sending your e-mails from, I'm sure they'll see your connection attempts and their log might explain why it's being silently rejected. Or it's a connection problem, but they would have this problem with some other company they communicate with, I guess.
I hope these are some ideas that will help
Regards