Yesterday I started a blitz game (https://online-go.com/game/6988965). After around 30 moves my opponent set the game on pause. I’ve waited for him for 20 or 30 minutes, and then left. At some later time he returned and resumed the game. It finished with my loss by timeout.
Question is: how to deal with such games? I am not blaming my opponent – for all I know, he had good reasons for a pause. But counting this game as my loss seams unfair.
Well, when I put a game on pause, I will personally notify the person that I’ll be resuming the game so that he doesn’t time out. Perhaps you could request your opponent to do the same for you as well. 
Add as friend and when both of you guys are online, you can continue the game. Or, if you’d would like a simpler solution- Play fast correspondence games or live games. (Honestly, I find it quite dishonest for someone to resume the game when the person isn’t around)
There is no way other than trust to deal with pause.
If you don’t trust your opponent then just unpause (resume) and continue the game (or win by timeout). If you have complete trust then you can keep it paused, play some moves it while it’s paused and then continue when you both seem to make enough moves at the same time frame(like constantly getting notifications). One will get notifications when it’s their turn to move. Just remember that there seems to be maximum pause period of 30 days or something. I’m not sure if it is refreshed after each move made.
If someone leaves for an “unreasonable” period of time - the definition of unreasonable depending on the type of game - then I would say it’s reasonable to message them in-game and directly that you’ll be unpausing the game if they don’t return. If they time out, then it’s on them for not being ready to play a whole live game. This is especially they case if they don’t even attempt to communicate why or for how long they need to pause the game.
If an opponent pauses a blitz game without communicating about it in any way it is fair to wait for e.g. the duration of a short phonecall or however long it takes to get the door. Imo anything beyond lets say… 5 -10 minutes tops is already unreasonable unless agreed on.
In any case it is always polite to try to notify your opponent that you are going to resume, especially in blitz games.
@Aengus It is good to assume that a pause was for good reason and it probably was, but at some point (the sooner if there is no communication happening) noone will blame you if you run out of patience or time yourself.