This is a known issue to users but Samsung won't admit it. I have a Galaxy Tab 4 7.0 and have the same problem. I have read a lot of other users experiencing the same issue.
I emailed, chatted and spoke with Samsung customer service about the issue. After a lot of back-and-forth, I finally set up a service ticket where I sent them my tablet, they replaced the entire motherboard, and sent it back to me. The Wi-Fi is integrated into the motherboard, and replacing the motherboard didn't fix the problem. This is the only device I use that has this issue, and it happens when connected to other networks as well (not just my home router, NETGEAR N600).
Basically, the Wi-Fi in the unit is garbage. The device shows that the device has a wireless connection, shows the SSID of the router, and shows full-strength for the signal- but the internet connection just stops working. No rhyme-or-reason, either. It will happen in the middle of doing something after working perfectly for hours. It normally won't fix itself, and the easiest way I've found to reconnect is to just cycle the Wi-Fi off and then on again.