If you want to connect a second controller to your Playstation 4 in order to play together in a team or against each other, one of the two controllers may lose its connection to the console after some time.
If this problem also applies to your Playstation 4, then fortunately it can be solved very easily as follows:
The player using the second controller must go to "New User" in the PS4 menu immediately after plugging in and then select "As Guest".
This will fix the problem and you can play with two controllers on Playstation 4 without any problems.