A bug in BSAdv 1.2 keeps Joomla from finding the next release. If you cannot update from 1.2:

  1.  From your Joomla web site back end, go to Extensions, Extension Manager, Updates. Purge Cache, Update.
  2. If the option to update to a new release still does not show up, download the temporary component com_bsadvfix. It is located in the Files section of JoomaCode. Installing this will fix the problem with 1.2 and allow it to find the new release. Uninstall this temporary component immediately after installing it.  The fix will remain.

Details:

There is an XML file that BSAdv uses to identify releases.  The URL that points to the XML file is stored in the jos_update_sites table.  The value used in BSAdv release 1.2 was:
http://bsadv.org/downloads/releases/bsadv-update.xml
but should have been:
http://bsadv.org/downloads/releases/bsadv-update2.xml

This bug keeps Joomla from finding the next BSAdv release.  You can use the temporary component provided to fix this problem, or you can use a program like PhpMyAdmin to make the change to the jos_update_sites table yourself.