Gulfstream 450 pilot reported the manual pressurization controller stopped functioning during descent and the automatic pressurization system was deferred; which resulted in complete loss of pressurization control. Flight crew donned oxygen masks and continued to destination and landing.

Narrative

As we were descending on the ZZZZZ arrival for ZZZ the manual pressurization controller appeared to stop responding and the cabin climbed to approximately 24000' The cabin Oxygen masks deployed and the crew donned the cockpit Oxygen masks. This happened in busy airspace and we had a temporary lapse in communication with ATC due to the noise from the mask microphone picking up the sound of the Oxygen flow and making it difficult to hear ATC and ATC was having difficulty understanding our transmissions. We were able to get a vector off of the arrival and continue descent to approximately 15000'. Crew communication was restored and we were able to rejoin the arrival and continue to the destination without further issue. I did not declare an emergency because by the time that we reestablished clear communications with ATC and between crewmembers we were in a position to proceed without assistance. Had communications been intelligible; we would have declared an emergency at the onset of the problem. Landed without further issue.Cause: The automatic pressurization system was found to be inoperative on Day 0 and was subsequently placed on MEL. While it is technically approved to operate the pressurization system in the manual mode; there is no more backup if it does not function correctly. Continuing to operate on a backup system and failure to take corrective maintenance action at the first opportunity caused this event. Company pressure to continue operations was also a significant factor.Suggestions: Fix maintenance items at the first opportunity. There were at least 3 opportunities to fix the problem instead of MEL. (ZZZ1; ZZZ2; ZZZ3)Remove the threat of punitive action for declining to fly.The aforementioned Maintenance issue was addressed with both chief pilots; Maintenance Control; Dispatch; and all wanted to continue scheduling trips on this aircraft with the known factors. Safety was contacted as well; but they were unable to get a response from those who they contacted regarding this issue.