I came across this problem on a web application that had been working fine, then all of a sudden the “Target Audiences” property disappeared from the web part tool pane.
To solve this problem I re-associated the web application with the Shared Service Provider (SSP) and bounced IIS.
1. Web applications are associated with SSP’s in central administration. Select Shared Services Administration
2. Select Change Associations
3. Select the web application you are having problems with, and select OK to complete the process.
4. Perform a complete IISReset.
Then the property miraculously reappeared – hooray!
ITS BACK!!
During investigating this issue I found the class responsible for rendering this section of the tool was an internal class WebPartToolPartAdvanced. I you really get stuck and my method doesn’t cut it you could dig around in that class and see if you can find anything that helps.
Edward Wilde 
[…] https://blogs.edwardwilde.com/2009/12/03/target-audience-property-not-displaying-missing-for-web-part… Bereitgestellt 2 Jul 2010 13:27 von Oliver Wirkus Gespeichert unter: SharePoint, How to […]
Looks like I found the solution for this problem. Was frustrated and got more confused with these misleading answers posted on the internet. Just follow these steps:
Central Admin -> Web Application General Settings -> Select your Web App (on which your site collection is hosted) -> Click on Service Connections from the top ribbon -> Check the User Profile Service Connection and save changes.
This should display the Target Audience property on your web part’s Advanced property.