What a dumb design decision. I don't even want to see anyone TRY to defend it.
While I haven't been too fond of it overall, there are specific instances where you lose the quests because they are story related (to those quests). Think in ME2 with some of the quests on Omega where you have two branching paths down the quests. Additionally, when you start taking on sidequests where you are favoring specific factions over others, definitely expect to lose out on some of the quests that you may be holding or hoping to get from other factions. This is especially true when its obvious that there is a direct conflict between the two sides.
As for the specific timer, generally speaking, most of the times you lose out on quests when you reflect on it, it makes sense why. There are a couple of head scratchers though.
With all of that said, most of these are just simple side fetch quests. Most of the major story quests or really unique side missions make it obvious that there is a chance of failure if you either delay to long in taking it or look at completing another mission (that's related) with another quest.
Edit - And I should mention that I can't recall a specific quest that after you are given it. makes you go do it and complete it within X time limit. It's not related to a specific 'timer' per se, but more about what you are doing and interacting with in the world.