Your IP is blacklisted for a reason, not just because you use Burp or Appscan. A possibility is that they have a mechanism to detect:
- Too many connections to the site
- An offending User-Agent
- Too many malicious HTTP requests
Try to discover first how or why it classifies you as malicious and try to circumvent then the protection.
Web sites does not usually blacklist IPs. Usually legitimate users do a lot of requests to a site so blacklisting them should easily would cause DoS events.
An offending User-Agent is a possibility, but I think with a low probability. Try changing the User-Agent to something friendly.
The last possibility, in the case it is really blacklisting your IP, is that they implement a WAF. The WAF is detecting malicious packets. Try WAF bypassing techniques to avoid the WAF blacklisting you.