In 13915a3100608f011b29da2f3716c990f523b631, the init flag is set before we even know if module initialisation was successful. Applying the following patch upon the aforementioned commit (in 3.8) fixes the issue for me on latest Debian:

```
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index 5261ed3d4c..782138e4e4 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -3250,17 +3250,14 @@ static int
 module_init(void)
 {
     PyObject *module = NULL;
+    if (module_initialized) {
+        return 0;
+    }
 
     asyncio_mod = PyImport_ImportModule("asyncio");
     if (asyncio_mod == NULL) {
         goto fail;
     }
-    if (module_initialized != 0) {
-        return 0;
-    } 
-    else {
-        module_initialized = 1;
-    }
 
     current_tasks = PyDict_New();
     if (current_tasks == NULL) {
@@ -3322,6 +3319,7 @@ module_init(void)
     }
 
     Py_DECREF(module);
+    module_initialized = 1;
     return 0;
 
 fail:
```