I have noticed this only since the latest update to the Note 3. Before when I left range of my home wifi the phone would go to LTE and upon returning home, automatically reconnect to my home wifi. Now it goes to 4g when I leave, but does not reconnect when I return home. Last night for example, I had been home for a couple of hours and wifi was still turned off and the phone was using 4g. When I manually turned on wifi, it connected immediately. I have played around with settings but can not seem to get it to reconnect automatically as it used to. Below are my advanced wifi settings. Thanks!
Sort by: Alpha
Keep on during sleep: Always
Always allow scanning: Unchecked
Auto network switch: Checked