First, the question: How is indefinite time to complete an objective handled, when it is not a question of skill, but a question of luck?

Example: Let's say that a character is attempting to unlock a door. The DC to unlock the door is 30. The character has a Open Lock modifier of 10, and therefore to open the lock it would require the character to roll a 20.

However, the character is under no pressure to open the lock. There is no risk of being caught. Theoretically, the character could spend hours, maybe even weeks attempting to open the lock. Now, the character - given enough time (and enough rolls) has the ABILITY to open the lock, it is just a question of how lucky he is on each attempt.

How are situations like this handled? Is it possible to simply bypass rolling the dice and for a DM to say something along the lines of, "After several long hours of attempting to open the lock, you finally hear a slight click."

Well, with the example given, it's sort of a question of skill and luck. And the current system has this very accurately represented: When a character has plenty of time to accomplish a goal, such as open a lock or disarm a trap, and they are not under duress, they are allowed to "take 20" on their roll.

As a result, their total skill is added to 20, allowing them to open locks they would not likely be able to open in a chaotic situation. If their skill is still not enough, they just don't understand that lock, and nothing short of a change of equipment, advancement in level, or special tools would help.

Thanks. I think that clears it up.