Check the file /etc/NetworkManager/conf.d/default-wifi-powersave-on.conf if the system uses NetworkManager. It contains wifi.powersave = 3. This configuration file came after 14.04 LTS.

To switch off the WLAN power save do:

1. Create a new configuration file with

   sudo nano /etc/NetworkManager/conf.d/system-wifi-powersave.conf
   

2. Put the following code in the file

   # File to be placed under /etc/NetworkManager/conf.d
   # File name lexically later than 'default…'
   [connection]
   # Values for wifi.powersave are 
   # 0 (use default), 1 (ignore/don't touch), 2 (disable) or 3 (enable).
   wifi.powersave = 2
   

3. Save the file with CTRL+O, leave nano with CTRL+X, reboot with sudo reboot now and check with iwconfig.

Further hints

• The name of the new file is important. It needs to be later in the alphabet than default-wifi-powersave-on.

• All WLAN connections are affected by this system-wide change.

• Each WLAN connection still can have individual power management settings. See the answer from AHAN in this thread.

Source: NetworkManager WiFi Power Saving

From the comment by @waltinator here's what I did. As of right now, it looks like this has fixed things.

Make a file in /etc/network/if-up.d called wifipower (the name doesn't matter):

sudo -H gedit /etc/network/if-up.d/wifipower

And write in it:

#!/bin/bash
iwconfig wlan0 power off

Save and make it executable with

sudo chmod a+x wifipower

Basically, every time a connection is established the script wifipower will be executed and turn power management off.