Huh?

Time quests can come and go as Playio pleases. So no guarantee they stick around when you go off the page, especially if they're marked as Limited Time, unless you accept them. The same time quest can return later though, sometimes with a different reward amount

I've had it happen before a few times. Usually I see them pop up later but doesn't always. Not sure if it's an intentional feature designed to make you panic accept and fulfill time quests or just a bug lol. But yea you're right, the recent time limited ones have been around for a long time. I assumed they were sticking around because I hadn't touched them (since from my experience the time limited ones do actually tend to go away) but good to know they'd stay regardless.