Ethernet connection drops for 10-20 seconds every 20 minutes

Once or twice an hour, my Ubuntu machine's ethernet connection will drop:

$ ping google.com
(nothing happens)

After 10-20s (though sometimes longer) it will magically come back.

During the outages, I'm unable to ping google.com or an IP, so I don't think it's a DNS issue. I've tried a number of things to debug:

1. Rebooted
2. Updated/upgraded all packages.
3. Uninstalled and re-installed network-manager.
4. Swapped ethernet cables.

My coworkers are connected to the same router as I am and they're not experiencing this issue, so it does seem to be something with my machine.

Any ideas? I'm fresh out of them and this is getting quite frustrating!

Here's a whole bunch of information about my system:

$ lspci
00:00.0 Host bridge: Intel Corporation Device 591f (rev 05)
00:02.0 VGA compatible controller: Intel Corporation Device 5912 (rev 04)
00:14.0 USB controller: Intel Corporation 200 Series PCH USB 3.0 xHCI Controller
00:14.2 Signal processing controller: Intel Corporation 200 Series PCH Thermal Subsystem
00:16.0 Communication controller: Intel Corporation 200 Series PCH CSME HECI #1
00:17.0 SATA controller: Intel Corporation 200 Series PCH SATA controller [AHCI mode]
00:1f.0 ISA bridge: Intel Corporation 200 Series PCH LPC Controller (H270)
00:1f.2 Memory controller: Intel Corporation 200 Series PCH PMC
00:1f.3 Audio device: Intel Corporation 200 Series PCH HD Audio
00:1f.4 SMBus: Intel Corporation 200 Series PCH SMBus Controller
00:1f.6 Ethernet controller: Intel Corporation Ethernet Connection (2) I219-V

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 17.04
Release:    17.04
Codename:   zesty

$ ifconfig
docker0: flags=4099<UP,BROADCAST,MULTICAST>  mtu 1500
        inet 172.17.0.1  netmask 255.255.0.0  broadcast 0.0.0.0
        inet6 fe80::42:e7ff:fe8d:d514  prefixlen 64  scopeid 0x20<link>
        ether 02:42:e7:8d:d5:14  txqueuelen 0  (Ethernet)
        RX packets 25739  bytes 1591975 (1.5 MB)
        RX errors 0  dropped 0  overruns 0  frame 0
        TX packets 116624  bytes 169185651 (169.1 MB)
        TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0

enp0s31f6: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
        inet 10.201.32.57  netmask 255.255.255.0  broadcast 10.201.32.255
        inet6 fe80::7285:c2ff:fe2a:efa8  prefixlen 64  scopeid 0x20<link>
        ether 70:85:c2:2a:ef:a8  txqueuelen 1000  (Ethernet)
        RX packets 1938458  bytes 1438227394 (1.4 GB)
        RX errors 0  dropped 0  overruns 0  frame 0
        TX packets 1442649  bytes 772299655 (772.2 MB)
        TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0
        device interrupt 16  memory 0xdf000000-df020000  

lo: flags=73<UP,LOOPBACK,RUNNING>  mtu 65536
        inet 127.0.0.1  netmask 255.0.0.0
        inet6 ::1  prefixlen 128  scopeid 0x10<host>
        loop  txqueuelen 1000  (Local Loopback)
        RX packets 181354  bytes 50978753 (50.9 MB)
        RX errors 0  dropped 0  overruns 0  frame 0
        TX packets 181354  bytes 50978753 (50.9 MB)
        TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0

$ ethtool enp0s31f6
Settings for enp0s31f6:
    Supported ports: [ TP ]
    Supported link modes:   10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
                            1000baseT/Full 
    Supported pause frame use: No
    Supports auto-negotiation: Yes
    Advertised link modes:  10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
                            1000baseT/Full 
    Advertised pause frame use: No
    Advertised auto-negotiation: Yes
    Speed: 1000Mb/s
    Duplex: Full
    Port: Twisted Pair
    PHYAD: 1
    Transceiver: internal
    Auto-negotiation: on
    MDI-X: on (auto)
Cannot get wake-on-lan settings: Operation not permitted
    Current message level: 0x00000007 (7)
                   drv probe link
    Link detected: yes

Here's something I see in /var/log/syslog around the time of a dropped connection:

Jul  7 12:44:02 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:03 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:04 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:04 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:05 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:06 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:07 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:09 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:11 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:11 dv systemd-resolved[1259]: Using degraded feature set (UDP+EDNS0+DO) for DNS server 10.201.1.18.
Jul  7 12:44:13 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:15 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:17 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:18 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:18 dv systemd-resolved[1259]: Using degraded feature set (UDP) for DNS server 10.201.1.18.
Jul  7 12:44:18 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.
Jul  7 12:44:20 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.18 for interface enp0s31f6.
Jul  7 12:44:22 dv systemd-resolved[1259]: Switching to DNS server 10.201.1.15 for interface enp0s31f6.