B300 King Air pilot reported cabin pressure climbing due to bleed air failure. Crew followed checklist; descended and continued to destination.

Narrative

At approximately XA:00; during the cruise portion of a King Air 350 flight to ZZZ; the crew received a right bleed-air failure indication. This system provides air for aircraft pressurization. Upon illumination of the Master Caution; the crew executed the appropriate checklist. Despite completing all steps; the cabin altitude continued to climb at an estimated rate of 2;000 feet per minute.At the time of the failure; the cabin altitude was approximately 6;000 feet; consistent with operations at FL250. The crew observed the cabin altitude approaching (but not quite) 10;000 feet. At that point; the remaining (left) bleed-air source was unable to maintain pressurization as a backup; and the cabin altitude continued to trend upward. Priority handling was requested; and ATC was advised of the pressurization issue. The crew requested and received a descent; initially to FL240; followed by a clearance to 10;000 feet at the request of the Captain to stabilize the cabin.All preflight and run-up procedures had been completed prior to departure; including bleed-air system checks; which were normal with no anomalies noted. The flight continued without further incident. No injuries occurred. The event was isolated to a pressurization system malfunction.