I'm new to this forum and new to the Galaxy S3 LTE version for about a week now but not new to smartphones. I'm in Canada and on the Rogers LTE network.
Having the exact same issues as Arkangil above so our phones are similar in behaviour. Basically my phone will connect successfully to my wifi network at home but will disconnect/reconnect frequently and sometimes fails to reconnect (with error failing authentication even though it hasn't changed) and have to force a reconnect by disabling WIFI and re-enablilng it.
I have determined that wifi works fine as long as the phone is plugged into a power source, however when running from battery is when I see the problem. I have disabled the general power save and enabled the feature to keep wifi always enabled.
I also already tried to use the procedure noted above in this thread to take phone into service mode and disable wifi power saving at the lower levels, however that procedure fails completely on my phone with the error message "UNKNOWN APPLICATION". Makes me wonder if it only works on a rooted phone or whether the LTE version of this phone differs much more than the international version of it.
I'm hesitant to take the phone back as everything else on the phone works well and generally really like this phone and features it provides.