Tried setting just speed 1000 duplex full - no difference.
After that set speed 1000 duplex full on a switch side - link down O_o.
After changing to 100 everything is working. 
Now set ETHTOOL_OPTS="autoneg off speed 100 duplex full" only on my side (and auto on a switch - standard port config)
No flapping so far on 100Mbps. I think I will use this workaround, still very strange why it doesn't work properly on 1000, I guess its a kernel module problem or something like that. If anybody still has any suggestions about 1Gbps - you are welcome :).

пн, 26 окт. 2015 г. в 21:47, Rick Stevens <ricks@alldigital.com>:
On 10/26/2015 11:24 AM, Kseniya Blashchuk wrote:
> I tried disabling autoneg, and it helped, but in this case dot1x auth
> doesn't work for some reason, I didn't have time to troubleshoot why,
> but there is no mac address on a switch port when dot1x is enabled.
> But i didn't try setting speed 1000 duplex full on a switch side. I'll
> try it tomorrow once again.

Not sure what's on the end of your dot1x, but it may be part of the
autonegotiation process to make that all work. You can leave autoneg
on to get by that, but still set the speeds and such once its done. That
may get squonked (new word) by future negotiations. Dunno.

> On Mon, Oct 26, 2015, 9:14 PM Rick Stevens <ricks@alldigital.com
> <mailto:ricks@alldigital.com>> wrote:
>
>     On 10/26/2015 09:57 AM, Kseniya Blashchuk wrote:
>      > Hi everyone!
>      > I noticed in dmesg that my ethernet link is flapping all the time
>      > [Oct25 18:55] r8169 0000:02:00.0 enp2s0: link down
>      > [  +3.131667] r8169 0000:02:00.0 enp2s0: link up
>      > [Oct25 18:56] r8169 0000:02:00.0 enp2s0: link down
>      > [  +2.763688] r8169 0000:02:00.0 enp2s0: link up
>      > [Oct25 18:59] r8169 0000:02:00.0 enp2s0: link down
>      > [  +3.060069] r8169 0000:02:00.0 enp2s0: link up
>      > [Oct25 19:00] r8169 0000:02:00.0 enp2s0: link down
>      > [  +3.559610] r8169 0000:02:00.0 enp2s0: link up
>      > I changed the cabling, tried to plug into another switch no
>     difference.
>      > Any ideas will be very appreciated as this flapping brings a lot of
>      > inconvenience.
>      > My device in lspci:
>      > 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd.
>      > RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 10)
>
>     Uhm, could be a kernel issue or a driver issue. Generally when I see
>     that sort of thing it's an auto speed or auto duplex negotiation between
>     the driver and switch that isn't working. You could try forcing the
>     speed and duplex via something like:
>
>              sudo ethtool -s enp2s0 autoneg off duplex full speed 1000
>
>     to set a fixed 1Gbps, full duplex connection and see if that helps
>     stabilize things. If that works you could try to restart auto
>     renegotiation via
>
>              sudo ethtool -s enp2s0 autoneg on
>              sudo ethtool -r enp2s0
>
>     The first comment re-enables autonegotiation, the second forces a
>     renegotiation.
>     ----------------------------------------------------------------------
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