Success!
I couldn't disable network-manager as advised because my linux pc is a headless server and if I stop the daemon my connection to the server fails.
However I managed to configure to bring usb0 up as soon as something is plugged in and then stop managing it, and now connection to the kindle is stable.
Code:
root@acerino:~# nmcli dev status
DEVICE TYPE STATE
eth0 802-3-ethernet connected
root@acerino:~# nmcli dev status
DEVICE TYPE STATE
usb0 802-3-ethernet unmanaged
eth0 802-3-ethernet connected
root@acerino:~# ssh root@192.168.15.244
Welcome to Kindle!
root@192.168.15.244's password:
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# N O T I C E * N O T I C E * N O T I C E #
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Rootfs is mounted read-only. Invoke mntroot rw to
switch back to a writable rootfs.
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Thank you kfc1 and NiLuJe and everybody else