Answer
Wifi adapters by default often come up in a power save mode. That is a mode in which the adapter shuts off the network connection in a state of inactivity.
While this is a good way to achieve additional power savings it of course introduces a delay for re-connecting.
To set the mode on or off:
iw wlan0 set power_save on
iw wlan0 set power_save off
To query the current setting issue:
iw wlan0 get power_save
Some systems might require "sudo" in front of the commands to be exectuted.