@Moderator
That port is capable of providing 2A at 5V from a SW controlled GPIO (GPIO_157).
I'm surprised you would experience a brown-out from a USB to ETH adapter.
On Voxl2, we provide a 10uF and a 1uF cap right at the 60-pin J3 connector.
If you are doing a custom adapter, and to meet USB3 specs, you should not need much more capacitance.
However, if you have a long length before your mating connector, a good 10-22uF would be wise.
We provide a 100uF cap on all of our USB ports that mate to Voxl2 (M0090 5G Modem Plug-in card, for example), but it is also due to a USB switch to help manage the ON time during enumeration.
Back to your specific issue, I would double check you are not toggling GPIO_157, or that your connection is solid and not intermittent.
I cannot find specific ETH dongle power consumption specs online, but it is likely using a LAN7801 or similar type device plus a PHY, which would not exceed more than a few hundred mA combined with magnetics:
a50456c1-db0d-4702-ab52-693715163dfb-image.png
b4d29526-d5e9-4dff-aeb6-760e4808daa0-image.png
So a brown out does not seem likely here. Even a 500mA USB2 rated device has no issue powering these types of dongles.