The code looks just fine so as you say it may be a port issue.
It could also be an ISP issue too as some ISP's don't like multiple repeat connects and may throttle a connection identifying it as a "BOT"
That is not the same in an industrial situation where some clients need to repeat connect for small data packets.
Do you really need every second ?
Or could you try getting the DNS from the source eg. router.
Have seen here with multiple Arduinos where I forgot to change the shield IP and it has been colliding with another Arduino and neither worked until I changed the IP.
Unlike an operating system the Arduino cannot tell you there is already an IP with that address and will happily try all day to compete with another IP.