Updater fails with the error during Plesk upgrade: "Autoinstaller busy".

Symptoms
Update with Server > Updater hangs for a long time and then reports error like:

Error: autoinstaller__status_known
Error: Autoinstaller busy.
Warning: Installation is in progress.

Cause
SWsoft Plesk panel times out waiting for response from autoinstaller utility (~5 minutes). It may happen because of high server load or very slow network connection between Plesk server and autoinstall.plesk.com repository server.

Usually this may happen with Plesk for FreeBSD versions starting from 8.1.0 and later, because it takes time for autoinstaller to download, extract and make indexes of SWsoft ports collection.
Resolution
Increase timeout values to greater ones (for example 30 minutes) in the Plesk panel server and Plesk panel PHP configuration files:

/usr/local/psa/admin/conf/httpsd.conf:
Timeout 1800

/usr/local/psa/admin/conf/php.ini:
max_execution_time = 1800

Then restart Plesk panel to accept changes and continue update.