The essence of the Rockstar Games anti-piracy is that the security system is activated periodically, and it does not occur on schedule, and goes in a totally random order. After activation of protection, there is authenticated version of the game. In case if you do not have a WAN connection, naturally the security system cannot be authenticated. Because there is a failure — an error that throws you out of the game.
It’s unpleasant, but, alas, there is no real solution to the problem, which would help with a 100% result to play in offline mode. There is only advice, and it is that after a successful authentication of the game, the security system will no longer be activated, which means that you can play even without an internet connection.