I think I finally found the fix for this issue. I needed to disable the AVB/EAV mode. This is a relatively new standard that reserves the Ethernet bandwidth for latency / jitter sensitive audio/video traffic to provide low-latency and low-jitter medium for that traffic. However, the Ethernet switch that the Ethernet adapter supporting this standard is connected to must also support this standard in order for this feature to work. Almost no consumer-grade Ethernet switches support this standard, and not even all Cisco enterprise-class switches support it. For example, Cisco 3560 Series switches (or lower-end / older switches) do not support this standard. This standard is supported in Cisco 3650, 3850, and 9000 Series switches.
So, when I disabled this standard under the Thunderbolt Ethernet adapter and re-enabled DHCP, the Thunderbolt Gigabit Ethernet adapter (built into the Apple 27" Thunderbolt Display) connected, obtained DHCP, and has been working for a week now without any issues. Please see the attached screen shot to see how you can disable AVB/EAV in macOS System Preferences -> Network.
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