Does the sender get an error message (like "undeliverable"), or does delivery fail silently?
Here's how you check your DNS and firewall setup. Check your MX record with:
nslookup -q=MX <yourdomain.com>
It should return a fully-qualified hostname (FQDN). If it does, run
nslookup -q=A <the FQDN returned by the previous command>
It should return the public IP of your VPS. Assuming the IP address is correct, run:
telnet <the IP address returned by the previous command> 25
If TCP port 25 is open, Postfix should respond with an SMTP message starting with "220".
If all these tests succeed, it's probably a Postfix configuration issue. If the sender doesn't get an error message, check the maillog on your mail server for clues.