I can confirm that the problem is between Apple Time Capsule (mine is 5th gen) and the linux driver of the usb ethernet adapter. I moved my raspi to another location where I connected it to ethernet switch and there was no connection losses.
I tried to downgrade Time Capsule fw (7.7.3 and 7.7.7), but it didn't help. Have to come up with another solution or use to old usb-ethernet adapter for now.