Games seem to go indefinitely.

[CPTNBob]

Even with a time restriction, it seems like people just pop out a trade and the timer stops until they decide to play again. Shouldn't there be a timer then on whoever is left to accept/decline trade, or the trade originator after everyone selects thier action?

[Cos-]

When someone suggests a trade, their timer stops and the other players' timers start, because it's now effectively the other players' "turn" until they choose to accept or reject. Each of those player's timers stops as soon as they click accept or reject. When all other players have clicked accept or reject, the timer immediately starts again on the player who offered the trade, because it's back to being their turn.

Nobody can stop the timer, they can only transfer it to other players, just like with finishing a move. When you complete your move, your timer stops until the other players have played (or they offer a trade). This is all exactly as it should be. It's doesn't work the way you describe. Just think of offering a trade, and answering a trade, as "turns".

And yes, this does mean a game of Catan has a lot more turns than some games where each player always does their whole turn all at once, without ever throwing it to other players and having to wait for their turns. But Catan is not the only game like this. For example, I play a lot of wingspan, where some birds have "pink powers' that activate when other players do certain actions, and some birds have powers you activate on your own turn that allow all other players to do something. If you take an action that activates other player's pink powers, or one of your bird's powers that lets everyone do something, your turn and your timer pauses, and you have to wait for each other player who gets to do something until they do it. Their timers run until they do their thing, because it's now effectively their move, even though it's in the middle of your turn.

This is just how BGA works.