diff --git a/deploy/nginx.conf.template b/deploy/nginx.conf.template
index 464cf1b..c84e6e4 100644
--- a/deploy/nginx.conf.template
+++ b/deploy/nginx.conf.template
@@ -3,6 +3,11 @@ server {
     listen 8080;
     server_name ${PUBLIC_HOST};
     if ($host != ${PUBLIC_HOST}) { return 400; }
+    # Resolve through Docker's embedded DNS at request time.  This prevents
+    # Nginx from exiting during a Swarm rollout when the API task is briefly
+    # unavailable or still creating its database schema.
+    resolver 127.0.0.11 ipv6=off valid=10s;
+    set $api_upstream api:8000;
     root /usr/share/nginx/html;
     index ${WEB_INDEX};
 
@@ -17,7 +22,7 @@ server {
     location /api/ {
         limit_req zone=api_limit burst=100 nodelay;
         limit_req_status 429;
-        proxy_pass http://api:8000;
+        proxy_pass http://$api_upstream;
         proxy_http_version 1.1;
         proxy_set_header Host $host;
         proxy_set_header X-Forwarded-Host $host;