All IPv4 stops working, IPv6 goes on. [Only under LEDE]

Just looking for some help to learn how to better troubleshoot and deal with this.

Sometimes, after a few days in, the IPv4 of my router goes down. I'm not sure this is the best phrasing to describe, so let me elaborate:

At first I didn't know what was going on, I would just think "my internet is down", because pretty much every website or service would stop working, and my go-to internet check is to ping Google DNS, which would also give me timeouts.

One time I was watching YouTube and it kept going even after everything else was down.
Oddly enough, I noticed that Google itself still worked, unlike almost every other website I knew.
Then it clicked: ping -> Reply from 2800:3f0:4004:804::200e: time=33ms

I could only access websites that provided native IPv6 access, namely, very few.
This happened in my desktop, under Win10, a laptop also under Win10, and a laptop with Ubuntu.
At first I believed this was an ISP problem, somehow.
I rebooted the ADSL modem and router and everything was fine for a while.

This was a year ago, in 2016, happened twice, about two months apart.
Back then I was using a ASUS RTN13U router with LEDE, unfortunately don't remember the version.

Now, in the last four months or so, the problem came back, sometimes being really really annoying, since not even rebooting the router fixes it. Just have to keep rebooting and hope it gets in a good mood and starts working again.

Now, I'm currently using a Linksys WRT1900AC running LEDE Reboot 17.01.4 r3560-79f57e422d / LuCI lede-17.01 branch (git-17.290.79498-d3f0685).
(Was with an older release, but updated a month ago to see if it'd help solve the issue. Apparently it did and helped for a while, but last night it happened again.)

I figured this wasn't an ISP problem because I could consistently take my laptop and plug it directly into the modem and manually connect (ADSL2+) and it would work fine every time. And if I just shut it down, and plug the router again - same problem, IPv6 works, IPv4 down.

I noticed that when this happens, I can't even ping the router - configured to - it gives me timeout.
Much less access it.
Watching anything on YouTube is fine.
Making any Google search is fine. (Good luck clicking in any result though, since 9/10 sites won't open, because ipv4)

Never had this problem before with any stock firmware, or any DD-WRT firmware on any of the 3 routers I've used in the past 6 years. In fact, no friend of mine has ever even heard of anything like this.
I'm no network expert by any means at all, but I'm a Computer Engineering grad student in my fourth year so I'm not entirely clueless either, just looking for some help, cause Googling this proved almost futile.

So... Any word of advice from anyone?
I thank you in advance for your time and consideration reading this far =)
(My apologies for any messed up wording, English isn't my primary language.)

It's a bit difficult to diagnose it, unless you can make some test while it is happening... My first guess is that there is another device in the network with the same address, or perhaps another DHCP server.

Thank you for the reply.

Had an informative (but weird) breakthrough - It happened again the other day, and while all the symptoms I described above remain true, I've noticed the oddest thing - my Android phone IPv4 seems to remain working.
I'm clueless as to how that may be. But the good thing is that I can now access the router, the html interface opens just fine on the phone, and I assume the shell would work too if I get Putty in the phone.

It amazes me how the desktop suddenly stops being able to even ping the router, and not the phone.
Naturally, one would just assume it's a problem with the desktop, but if I boot up my laptop - very same issue.
Can't even ping the router.

The good part is that now I can probably "make some test while it is happening".
Does anyone have any suggestion of what should I 'test for', or what should I be aiming to find?

About another DHCP server I find it unlikely, because there's really very few devices on the network.
Usually it's just my desktop, my phone, and a chromecast. (Apart from the router, and a modem configured to bridge mode)

I'll keep trying to figure this out and post here if I find out anything, but I'm all ears if anyone has any suggestions.

Have a nice day all

I think android devices typically still default to ipv4 because ipv6 is not fully supported (no dhcpv6), so your pc gets an ipv6 address but not your phone.
Are you running any addon LEDE packages that might cause issues?