diff --git a/src/H5T.c b/src/H5T.c
index b5e23452ca..b2137e752c 100644
--- a/src/H5T.c
+++ b/src/H5T.c
@@ -4133,7 +4133,8 @@ H5T__free(H5T_t *dt)
             for (i = 0; i < dt->shared->u.compnd.nmembs; i++) {
                 dt->shared->u.compnd.memb[i].name = (char *)H5MM_xfree(dt->shared->u.compnd.memb[i].name);
                 if (H5T_close_real(dt->shared->u.compnd.memb[i].type) < 0)
-                    HGOTO_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL,
+                    /* Push errors, but keep going */
+                    HDONE_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL,
                                 "unable to close datatype for compound member");
             }
             dt->shared->u.compnd.memb   = (H5T_cmemb_t *)H5MM_xfree(dt->shared->u.compnd.memb);
@@ -4170,12 +4171,14 @@ H5T__free(H5T_t *dt)
     /* Close the parent */
     assert(dt->shared->parent != dt);
     if (dt->shared->parent && H5T_close_real(dt->shared->parent) < 0)
-        HGOTO_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL, "unable to close parent data type");
+        /* Push errors, but keep going */
+        HDONE_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL, "unable to close parent data type");
     dt->shared->parent = NULL;
 
     /* Close the owned VOL object */
     if (dt->shared->owned_vol_obj && H5VL_free_object(dt->shared->owned_vol_obj) < 0)
-        HGOTO_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL, "unable to close owned VOL object");
+        /* Push errors, but keep going */
+        HDONE_ERROR(H5E_DATATYPE, H5E_CANTCLOSEOBJ, FAIL, "unable to close owned VOL object");
     dt->shared->owned_vol_obj = NULL;
 
 done: