Note: I'm posting this workaround as an answer due to the number of times this has been reported as a bug only to expire shortly thereafter and resurface again.

Test

1. Enter Ubuntu recovery mode: a. Power on system and press Shift during boot up for GRUB menu.

   b. Choose "Advanced options for Ubuntu" > Ubuntu, [kernel version] (recovery mode)

2. Choose "root" and key in below commands:

   rmmod forcedeth
   modprobe forcedeth msi=0 msix=0
   exit
   

3. Choose "resume" to resume normal boot

Now the network should be OK till next boot with AM3+ CPU.

If the workaround works on your system, please modify below file to automatically run the script when boot up:

Bug Workaround Solution:

1. Add the line exec rmmod forcedeth at next line of "script" (above grep?) in the file /etc/init/module-init-tools.conf or /etc/init/kmod.conf)

2. Add the line modprobe forcedeth msi=0 msix=0 to /etc/rc.local

3. Restart the system to verify

Sources: Primarily Achkap post #16 http://ubuntuforums.org/showthread.php?t=2020571&page=2

https://bugs.launchpad.net/ubuntu/+s...x/+bug/1003297

https://bugs.launchpad.net/ubuntu/+bug/1264509

https://bugs.launchpad.net/ubuntu/+source/linux/+bug/1281930

Clue from Julian Uribe in comments.

So I think I fixed the problem now. If the dropout does not occur within the next days, I'll mark this thread as solved.

I tried multiple strategies that have been posted on different sites. Maybe it would just be enough to install new drivers ( -> paragraph 5), but I'll list up everything in did, just in case there might be dependencies:

1. Ignore IPv6

(No direct success)

source: https://ubuntuforums.org/showthread.php?t=2288456

Click on Network Manager -> Click 'Edit' -> Edit the wireless connection -> Click the IPv6 tab -> Set IPv6 to ignore -> click OK -> Reboot.

2. Edit wifi-resume.service

(No direct success)

source: wifi still sleeping when resume

gksudo gedit  /etc/systemd/system/wifi-resume.service

Add the following:

[Unit]
Description=Local system resume actions
After=suspend.target

[Service]
Type=oneshot
ExecStart=/bin/systemctl restart network-manager.service

[Install]
WantedBy=suspend.target

close the text editor.

Now do:

sudo chmod +x  /etc/systemd/system/wifi-resume.service
sudo systemctl enable wifi-resume.service

reboot

3. Configurate Driver

(No direct success)

source: 16.04 LTS wifi connection lost randomly every 5 minutes

1. Get details of your PCI wireless card by running sudo lshw -class network
2. Get your card model info according to the product line. For instance, as you can see in the question description it says product: RTL8723BE PCIe Wireless Network Adapter so the model of my card is RTL8723BE
3. Open or create /etc/pm/config.d/config and add SUSPEND_MODULES="rtl8723be"(replace rtl8723be with your own model number) Then run echo "options rtl8723be fwlps=N" | sudo tee /etc/modprobe.d/rtl8723be.conf and reboot.

Now your system should be able to reconnect automatically after sleep, and wifi connection never got lost once for me after doing this.

4. Install other drivers

(No direct success)

Source: https://medium.com/@elmaxx/rtl8821ae-wifi-drivers-in-ubuntu-16-04-4c1286524afa#.dsczz2t2w

Check, if your card is one of the following models: rtl8192ce, rtl8192se, rtl8192de, rtl8188ee, rtl8192ee, rtl8723ae, rtl8723be, and rtl8821ae

lspci | grep Wireless

Then:

sudo apt-get install linux-headers-generic build-essential git 
git clone http://github.com/lwfinger/rtlwifi_new.git
cd rtlwifi_new
make
sudo make install
sudo modprobe rtl8821ae

Reboot.

5. Again, install different drivers

(Success!?)

Source: Dropping Internet connection on Realtek Semiconductor Co., Ltd. RTL8821AE

sudo add-apt-repository ppa:hanipouspilot/rtlwifi
sudo apt update
sudo apt install rtlwifi-new-dkms