What I did:
$ cluster/kube-down.sh
$ hack/dev-build-and-up.sh

(I saw this error:
ERROR: RESOURCE_ALREADY_EXISTS: The resource 'projects/seventh-circle-487/zones/us-central1-b/disks/kubernetes-minion-1' already exists
That's not what this issue is about, though)

Request https://$APISERVER_IP/api/v1beta1/pods

Got this error:

Internal Error: &url.Error{Op:"Get", URL:"http://kubernetes-minion-1.c.seventh-circle-487.internal:10250/healthz", Err:(*net.OpError)(0xc2101dcc40)}

APIserver should not fail to respond to GET /pods just because one of the minions is wedged.