Why ABDA kept fighting after Singapore fell

Should the ABDA fleet have withdrawn after the fall of Singapore?

Not necessarily, because it was one of the few forces able to delay Japan and buy time for Australia to organise its defence.

After Singapore fell, ABDA was one of the few forces available to obstruct the Japanese advance. The case for continuing the fight depended on the immediate need to strengthen Australia's defences. Preserving ships for a future campaign competed with that urgent demand for time. Decisions therefore had to reflect the threat perceived by commanders then.