What can affect wi-fi, so that with a certain SSID, there is no connection with the router?

Question

WiFi

Colleagues, faced with garbage, which I can not explain.
Wi-fi ADSL router (Dlink DSL-2741B). Raised Wi-fi with SSID "Ashitaka", there is encryption, but this does not affect the final result. The computer connected via LAN (wire) works fine, no problems. When trying to connect to Wifi, phones (iOS, android) write, they say the password is saved, the network is known, but they do not connect (no errors are given). Mac OS the first two times when trying to connect gives out "wrong password", then it comes in and does not receive an IP (when you try to configure IP with handles, there is still no ping to the router).
We change the router (more precisely, we don’t change it, but simply use the old one as an ADSL modem), we raise the same network, with the same name and we have exactly the same picture. Turn off the password on Wi-fi - the same thing, change the password - the same thing ...
We change the SSID (network name) and everything becomes normal (On both Routers.). Everyone connects, gets an IP, no glitches.
Question - Can anyone give a clear explanation of what is happening?
UPD - It's not about the saved profile - it was reset, and new devices were also connected to the network.
UPD2 - This is not a second network with the same name, and also not a repeater (in both cases, the range was scanned).