diff --git a/src/jsonrpc.ts b/src/jsonrpc.ts
index 8975933..fea5248 100644
--- a/src/jsonrpc.ts
+++ b/src/jsonrpc.ts
@@ -654,12 +654,16 @@ export class ServerPool {
         this.session = session;
         this.options.session = session;
 
-        // Update session for all existing connections
+        // Update session for all existing connections and their transports
         for (const conn of this.pool) {
-            (conn as any).session = session;
+            if ((conn as any).transport) {
+                (conn as any).transport.session = session;
+            }
         }
         for (const conn of this.used) {
-            (conn as any).session = session;
+            if ((conn as any).transport) {
+                (conn as any).transport.session = session;
+            }
         }
     }