I just got my phone replaced under warranty for this issue and the new one is having the same problem as the old one. I think I figured out the issue though. I had my router set up to have my 2.4ghz band and 5ghz band using the same SSID and I would constantly get connected, get the unstable error, disconnect, and then reconnect. This was happening literally once a minute or more frequently. As soon as I changed the 5ghz band to a different SSID and connected only to that network, my disconnects and errors stopped. To me that means, it appears to believe your connection is unstable when it can bounce between the 2 bands because they use the same password and SSID. Like it connected to 5ghz, and then suddenly it was on 2.4 and then back on 5 and it had a mini-aneurysm or something.
This fix won't do me much good at work since I can't switch all of the SSIDs at the job sites to accommodate my phone, but at least it may be a start to finding a permanent fix.
There is no problem with having 5ghz and 2.4ghz on the same SSID. The issue is with the 5ghz band and likely the higher channels. When sharing a SSID your phone will connect to whichever frequency is the strongest.
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---------- Post added at 07:15 AM ---------- Previous post was at 07:10 AM ----------
Interesting - I too have an Asus router (RT-N66U) and have the contact "connection unstable" messages.
I wonder if this is possibly an Asus issue and not a Samsung issue?
There is an option you need to turn off on your 5ghz settings on the Asus. Wireless - Advanced - Professional - Explicit Beam forming to Disable.
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