USB 3.0 to Gigabit Ethernet Adapter with Realtek 8153 Chipset on macOS Catalina
Although the Anker USB 3.0 to Gigabit Ethernet adapter that is equipped with the Realtek 8153 chipset works out of the box with macOS Catalina 10.15.4, the adapter stopped working after waking up from sleep mode. Disabling DHCP and setting addresses manually didn't resolve these issues. While it was possible to remove and re-add the adapter in the network system settings to get it working again, this workaround only fixes the problem temporarily until the next sleep-wake event.
The suggestion to download and install the latest official Realtek driver for macOS 10.6 to 10.15 from realtek.com resolved the issue for me. Specifically, driver version 1.0.20 that was released on 2020-03-05 resolved the connectivity issues permanently after installing the driver, restarting the computer, and removing as well as re-adding the adapter in the network system settings once and for all. Manually unloading and loading the driver on the command-line as suggested in this thread wasn't necessary.