I’ve set the limit in wp-config.php and php.ini to 512MB, but it does not seem to have made any difference. The same error occurs. There do not appear to be any processes using any significant amount of memory, certainly nothing near the limit.
Since making this change the debug log now appears to include some errors:
[23-Dec-2015 21:33:51 UTC] PHP Warning: Illegal string offset ‘length’ in /var/www/wordpress/wp-content/plugins/jetpack/class.json-api-endpoints.php on line 1182
[23-Dec-2015 21:33:51 UTC] PHP Notice: Uninitialized string offset: 0 in /var/www/wordpress/wp-content/plugins/jetpack/class.json-api-endpoints.php on line 1182