Does the CXUHD have a 'Resume Play' function?

Yes, the CXUHD supports multi-disc resume play. It will resume play up to 5 discs. If a sixth disc is inserted, the first will then be forgotten.

Some Blu-ray discs support resume play and others do not. This is dependant on the individual Blu-ray disc. If the disc supports it, the CXUHD will also resume play a Blu-ray disc.