So when you leave the site, you accumulate APs with the default cool-down.
Make it so, when you do certain actions in-game, give some extra AP.
Ie. I visit the war room, then I buy something from market, after that add lets say 10 extra AP.
It could be animated, like when it adds to the bar you see some sparks around it, so you notice it happened.
You could fiddle with what should give a bonus, how frequently etc.
This could not only motivate people to spend some time online, but one step towards making it possible to be able to do something continuously.