Why are DNS server addresses lost after reboot?

As an alternative to the answer in the comments attached to the question (which you have already stated is your solution), I can only offer to others that do not use DNSCrypt that find similarly described symptoms. What fixed the problem for me, which was exactly as you described: after adding DNS servers and closing and reopening System Preferences and the Advanced section of the Network Control Panel, the DNS server list would not retain its data, took me time and effort to discover. PEBKAC: I was closing System Preferences without clicking the Apply button, which you will only see once leaving the Advanced section of that Control Panel. Hope this helps!