Router disconnecting + phantom wifi

> Model: R6400v2|AC1750 Smart WiFi Router-802.11ac Dual Band Gigabit

   Firmware version?  Some folks have reported wireless problems after a
firmware update.  Installing some older-version firmware might be an
interesting experiment to run.

> Starting about 2 weeks ago, [...]

   Any chance that the firmware was updated about two weeks ago?

> Logging into the router (www.routerlogin.net) gives an error message
> saying that my device isn't connected to the router's wifi network.

   Welcome to what may be the worst error message in the world.  For an
explanation, try:

      https://community.netgear.com/t5/x/x/m-p/1365830

   Briefly, the idea is that "[www.]routerlogin.net" should point to
your own router, but that's true only if you use your own router for DNS
name resolution.  Irregardful, you should be able to get to the thing
using its IP address, if you can determine (or guess) that.  Perhaps:
"192.168.1.1".  You can often get it from your computer's IP
configuration as the default gateway or router address (or some similar
description).

> Ocassionally, that login link will take me to a Linksys site, even
> though we have no Linksys equipment.

   That suggests that (at least occasionally) you're not really
connected to your own router.  Connecting to some other router would
evade your Netgear router's special handling of the
"[www.]routerlogin.net" name, and that could easily lead you to that
useless/misleading error page.  For now, I'd suggest not using that
"[www.]routerlogin.net" name, and sticking with the the router's LAN
address ("192.168.1.1", I'd guess).

> By the end of the day, I'm back to not being able to log in.

   Does that mean you're back to getting the same "You are not connected
[...]" error page?

> At one point, I even unplugged the ethernet cable connecting the modem
> to the router ... and I still had wifi access, which suggests that my
> router is not actually providing wifi at least some of the time.

   Define "still had wifi access".  If you still had access to the
outside world, then you had to be connected to some other router.  Even
if the router's disconnected from the outside world, you should still
have access to the router's own web site ("[www.]routerlogin.net" or
"192.168.1.1").

   As described, your symptoms are confusing (to me, at least).  My
guess is that some problem with the router is causing it to lose contact
with your wireless devices after it's been up for some time.  A quick
skim over these forums should find many similar complaints.  At that
point, your devices might be getting connected to some neighbor's
(Linksys?) guest/insecure wireless network, and more confusion ensues.

   As a (should-be-harmless) diagnostic aid, you might try changing your
router's LAN IP address to something other than "192.168.1.1".  Perhaps:
ADVANCED > Setup > LAN Setup : LAN TCP/IP Setup : IP Address.  I'd
suggest something odd-ball, like, say, "192.168.23.1".  You'd probably
need to restart everything after such a change.  The benefit would be
that when some gizmo gets confused and/or dis/re-connected, you could
look at its IP address and see if that ".23." (or whatever) is in there.
You may still find yourself connected to some stray Linksys (or other)
router, but, if that happens, then I'd bet that you won't see a ".23."
in your IP address, so you'll _know_ that you're not connected to your
own router.

   Of course, if you make that change, then you'd need to use that new
address to reach your router's administration web site, instead of
"192.168.1.1".  The router should redirect "[www.]routerlogin.net" to
the new address, but, if you were having trouble with that before, then
you'd still be wise to stick with using the (new) address instead of
that name.

   None of this (except, perhaps, a firmware-version change) will fix
the actual problem, but you might get a slightly less scrambled set of
symptoms.