There is some text about this in the DMG, although it is only related to "searching the room" - check out page 41.
I see no problem to let my players take 20 when they can retry and have a plenty of time and advise you to do the same.
Yeah. Sounds reasonable.DMG said:Unless the characters are under a time constraint, assume that they’re going to roll a 20 eventually
You technically can't take 20. I can't remember if I read this in the PHB or a CS told me, but it was an issue in my game so I remember finding out... somehow.
The reasoning being is that every skill supposedly has a chance to fail.
The problem with this is that it also specifically states under lockpicking (as one example) that you can't fail at it and can retry as many times as you like.
If a player fails a roll. that SHOULD mean he couldnt accomplish the task.