CMC and CRC isn't the same illness. A persistent yeast overgrowth doesn't mean people have CMC. It is demonstrated that after Antibiotic intake, yeast colonize the intestines.
These yeast colonies, one time established, can drive the necessary immune response to eradicate them. If the immune suppression mechanism is caused by mannan or Th17 down-regulation, it isn't totally clear yet.
At the end, the only solution is to eradicate the yeast colonies living in the gut. If these colonies continue to inject immune suppressors in your blood, you will never be able to recover the immunity. The immune deficit is acquired and caused by the same candida albicans.
However, CMC isn't necessary an acquired immune deficit. It may be a genetic or native immune defect.