Could Austria-Hungary rescue Goeben from Greece?

Why couldn't the Austro-Hungarian fleet sortie to protect Goeben after she entered a Greek port?

It was too far away, faced an unfriendly neutral Italy and other Allied forces, and would not risk much of the fleet to save one German battlecruiser.

By the time a damaged Goeben enters a Greek port, the Austro-Hungarian fleet is too distant to intervene effectively. Any sortie would have to contend with Italy, whose formal neutrality did not translate into sympathy for Austrian naval movements, as well as nearby French forces. Austria-Hungary also lacks a strong fast force positioned to reach the engagement. Sacrificing much of the fleet to save one German battlecruiser would therefore be an unattractive bargain.