I see one of the two recommended priority nodes for monerod has been changed from node.supportxmr.com to p2pmd.xmrvsbeast.com. It seems that when a priority node is down, monerod doesn't start, which can be fixed by temporarily removing the offending --add-priority-node parameter (correct me if I'm wrong).
Your monerod should have it's own node list, especially if it has been on the network for some time. A priority node being offline should not affect your node.
I mean, when I try to start monerod, monerod fails to start if sample.net in --add-priority-node=sample.net is down. I experienced that a few times, though it's just me.
FYI: According to Github pages, v3.6 doesn't start on some OSes (e.g. CentOS, Windows 7) perhaps as an accidental side effect of the compiler change; fixed in v3.6.1.