Answers:
从14.04升级到16.04.1之后，我刚刚遇到了完全相同的问题（在这种情况下，USB网络共享可以正常工作多年）。
基于syslog，它看起来像是与ModemManager冲突引起的。
Aug 25 13:12:24 outback NetworkManager[2543]: <info> [1472145144.1334] device (enp0s20u2): Activation: successful, device activated.
[...eliding log entries related to nm-dispatcher services]
Aug 25 13:12:38 outback ModemManager[2503]: <info> Creating modem with plugin 'Generic' and '2' ports
Aug 25 13:12:38 outback ModemManager[2503]: <info> Modem for device at '/sys/devices/pci0000:00/0000:00:14.0/usb3/3-2' successfully created
Aug 25 13:12:41 outback ModemManager[2503]: <warn> couldn't load Manufacturer: 'Serial command timed out'
Aug 25 13:12:44 outback ModemManager[2503]: <warn> couldn't load Model: 'Serial command timed out'
Aug 25 13:12:47 outback ModemManager[2503]: <warn> couldn't load Revision: 'Serial command timed out'
Aug 25 13:12:50 outback ModemManager[2503]: <warn> couldn't load Equipment Identifier: 'Serial command timed out'
Aug 25 13:12:50 outback ModemManager[2503]: <warn> couldn't load Operator name: 'SIM failed to handle CRSM request (sw1 106 sw2 130)'
Aug 25 13:12:54 outback ModemManager[2503]: <warn> couldn't load IMEI: 'Serial command timed out'
Aug 25 13:12:54 outback ModemManager[2503]: <info> Modem: state changed (unknown -> disabled)
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.3879] device (enp0s20u2): state change: activated -> deactivating (reason 'connection-removed') [100 110 38]
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.3881] manager: NetworkManager state is now DISCONNECTING
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.4362] dns-mgr: Writing DNS information to /sbin/resolvconf
Aug 25 13:12:54 outback dnsmasq[4348]: setting upstream servers from DBus
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.4430] manager: (ttyACM0): new Broadband device (/org/freedesktop/NetworkManager/Devices/4)
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.4441] device (ttyACM0): state change: unmanaged -> unavailable (reason 'managed') [10 20 2]
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.4445] device (ttyACM0): modem state 'enabling'
Aug 25 13:12:54 outback NetworkManager[2543]: <info> [1472145174.4457] device (enp0s20u2): state change: deactivating -> disconnected (reason 'connection-removed') [110 30 38]
我通过以下命令禁用了ModemManager：
sudo systemctl disable ModemManager.service
然后重新启动。从那时起，我随后的USB网络共享会话一直稳定。
我敢肯定有一种方法可以为我的手机（LG G3）正确配置ModemManager，但是我目前不需要串行调制解调器，所以这种方法对我有用。
对我来说，此命令有效：
sudo systemctl stop ModemManager.service
使用disable代替而stop不起作用。然后我重新打开NetworkManager：
sudo NetworkManager