Captain reported loss of cabin pressure control during cruise. After running the QRH procedures; the flight crew switched to #2 auto system and regained control and then continued to destination airport.

Narrative

In cruise at FL380; we got a CABIN ALT message. After cancelling the warning we looked at the Cabin Altitude Indicators; and realized the cabin had slowly risen to 10;000 feet and set off the warning. After donning our O2 masks and beginning the immediate action items; with the First Officers consent I decided to descend to FL340 and see if the controller could handle its job at a lower altitude. The cabin rate had been fluctuating between a slight climb and descent; so it seemed that the system was attempting to lower the cabin altitude. We didn't see any improvement in performance at FL340; so we decided to try switching to the Auto 2 system. That fixed and stabilized the problem.I called dispatch and maintenance via ZZZ1 radio. We mutually agreed that the problem seemed fixed and continued to ZZZ2 without incident.My question is why didn't the airplane recognize this as a failure of the Auto 1 system and automatically switch to Auto 2? Also; why do we not have a different checklist for Rapid Depressurization and Cabin Alt message? The Pressurization System did not recognize this as a failure of AUTO 1 and allowed the cabin to rise to 10;000 feet with automatically switching to AUTO 2. I think having a separate Quick Reference Handbook procedure would be helpful for this situation where the airplane is not depressurized; but is merely having a system failure.