Hi eggerda,
This message means that either your IP address or email address has been placed on a Blacklist (sometimes known as a Blocklist). Which is why you are unable to send outgoing mail (Suspected spam message rejected).
You mentioned that you have checked Spamhaus , but it's also possible that one of the other blacklist sites have you listed. To check the others please try the following.
On the connection you are unable to send email from, go to whatismyipaddress.com and it will provide you with your IP address. Grab that IP address and plug it into mxtoolbox.com/blacklists this tool will check your IP address against over 100 DNS based email blacklists to see if you have been blacklisted.
If you are follow the instructions provided as to how to get yourself de-listed.
How did this happen?
Basically, one of the 100 or so blacklisting sites, has detected undesirable activity in relation to your service blocked it. Most IP addresses are listed as a result of directly sending spam or viruses to special detectors (spamtraps) or by initiating SMTP transactions that look similar to viruses or botnet-proxies.
What Can I Do?
If you find your IP has been listed your system is very likely compromised by a virus either via mail, the web, or other download. So the first step is to determine whether your computer or any other devices connected to your service is sending out spam or infected by a virus. If you’re absolutely sure that nothing under your control is sending out spam or has a virus, then visit the blacklist removal page and request the removal of your address.
Alternatively, if you use an ADSL or NBN connection powercycling*# of your modem should resolve this issue as the IP address are dynamically assigned, so when the modem reconnects it will be given a new IP address.
I can’t stress enough how important it is to verify that you’re not actually sending spam. In many cases if your IP address has been blacklisted, the cause is a device within your own home or office network, which has been compromised and is sending spam. If you don’t fix the spam sending problem, then any attempt to move to a new IP address or de-list your listing will quickly fail and may lead to more severe listings.
Please visit spamhaus.org/xbl for more information
Hope this helps.
* Turn it off, wait 2 minutes, then turn it back on.
# This will not work if you are using a Telstra Internet Direct connection as your IP will be static and stay the same. You will need to contact the blacklister and request a de-listing.