PPPD keeps resetting

That's already set to 1. I can increase echo interval and tries for now but I would rather find the underlying issue

Check the logread when it fails at gigabit - is it same down and up?
About intel cards - check knobs around pause frames (-A), try those off
and eee (--show-eee --set-eee) , this sometimes drops to a speed that it cannot rise back, like 10mbps, and when you disable 10 and 100mbps advertise it magically goes working.

OK couple new information

When I first set to 1G mode I did a speedtest to see if my download speed was affected by it. Right after that the NIC stopped and PPP was restarted.

I then switched to 2.5G mode and I tried speedtest again. After 2 consecutive tests I got a PPP restart due to 5 echo fails but no NIC fail.

Now I switched back to 1G (still advertising 10/100 though) to try to get the data @breda4 requested. I have been trying speedtest left and right but so far couldn't reproduce. Was it luck? I don't know, I'll keep trying.

As for the data requested

root@OpenWrt:~# ethtool -a eth2
Pause parameters for eth2:
Autonegotiate:	on
RX:		on
TX:		off
root@OpenWrt:~# ethtool --show-eee eth2
EEE settings for eth2:
	EEE status: disabled
	Tx LPI: disabled
	Supported EEE link modes:  Not reported
	Advertised EEE link modes:  Not reported
	Link partner advertised EEE link modes:  Not reported

These look OK to me no? I can disable pause frames on RX but EEE disabled should be the way to go If I understand what it is correctly no?

You can try ethtool -A eth2 rx off tx off ; ethtool -r eth2 but that is still not cause of flop.