My Galaxy Note 10.1 kept loosing my known WiFi connections and password since about a week ago which really drove me crazy since I'm using
Passwords nobody can ever remember.
I've been searching the Internet for a solution for about 3 days now and I'm starting to think that even here in this thread we have not one but a few different problems, which need different solutions.
My Note did forget the WiFi settings every time it got disconnected, no matter whether I rebooted, changed location or toggled WiFi in the notification bar. In Google's product forum I found a topic with a similar problem on a nexus 5 and the tips suggested were the same as here, synchronisation related.
However, last entry someone suggested examining wpa_supplicant.conf in /data/misc/wifi (you need to be root for this)
Indeed, while file permissons were plausible the file size was zero bytes on my note.
I simply renamed the file with WiFi off then rebooted and turned WiFi on again.
Of course, one has to enter networks and passwords once more manually, but now they're stored again and my problem is solved.
So, if your problems with forgotten WiFis are sporadic, the problem might indeed be sync related and I suggest to turn off Samsung Sync and Google Sync in the Settings for a testdrive.
If, however, your device keeps forgetting Networks all the time or rather everytime it needs to authenticate again, I'd suggest examining the wpa_supplicant.conf.
The latter problem can only be solved with root access or by wipe of your device, I'm afraid.