Okay, you have to go get the Mc Guffin!!! It's done alot in RPG games, so let's look at it. Also, there's a short version down the bottom of this post!
The thing is, as a player you have absolutely no idea how to. You're trying stuff, but it seems to arrive at dead ends. Or maybe what you're trying to do takes a really long time to do in RL playing time - kind of a dead end by the slowing down of how long the act takes to execute in the fiction in RL time.
This is an issue with most traditional RPG's - there is no fail condition. No explicit point jumps out and says 'well, you can't try anymore, it's too late, you've lost'. So you keep trying this or that and they don't work, but neither does the game. Thou art in limbo!
A primary issue is that yeah, the fiction tends to give no fail condition. If you're standing in front of some puzzle door, unless the ceiling was coming down slowly, there's nothing that says that once you've tried something and it didn't work, you are that much closer to failing or have failed.
Which results in a sort of RPG blue screen. A limbo.
Some traditional RPG advice is to have the players be able to move onto something else. Indeed in classic AD&D, if you can't find the hidden treasure in dungeon room...well, the players can just shrug and say they go to the next room. Which works out great.
But you/the players have to go get the Mc Guffin!
About the only solution is to explicitly make clear that it is valid for the players to just give up.
Let's not treat "Well, we've gotten to near the end of the night soooooo....we'll just have what the players just did in the last thirty minutes solve the issue, even though if they had done that at the start of the session it wouldn't have worked!" as if it's a perfect solution. If the play session is four hours, that means pretty much any solution works, as long as you sit out the four hours and just suggest anything in the last thirty minutes. Well, I guess I can only argue from my own preferences, but as much, that's not something I desire anyway.
Of course the problem with players giving up is what if some do just want to admit defeat, but others just gotta try more things, and more things, and more!
I really am not sure. Perhaps players who have given up can head out early, or they can sit in at the game table but they don't have to try and wrack their brains anymore, they can just watch the other players. Basically you don't want someone to feel they are stuck unable to know what to do next, but also unable to simply give up and move on.
The other problem is, potentially, session time. You might have four hours to play, yet what if the players give up two hours in?
At that point the whole 'well, their actions can't make them fail' probably starts to look attractive, as if the RPG blue screen actually is how you play, since it will indeed fill in the time. It's just a question of what it fills it in with.
I would suggest a secondary optional goal, that you don't introduce at the start of play but merely hint at the possibility of ("There may be an extra mission to perform latter on - they'll send a message if there is"). If the primary goal has been completed, failed, or the players have given in and admitted defeat on it, then you can bring in the secondary optional goal to pad out the session time.
Lets be explicit though - this is an optional goal. If the players don't want to take it up, then they don't. If they have to play it, it doesn't escape the RPG blue screen problem really, as the players are now stuck with another problem because they couldn't solve the prior one.
1. Tell players they can simply admit defeat on their pursuit of the Mc Guffin. Those who do can retire from the table or sit and watch the others, but they no longer have to run their PCs (whether they can offer suggestions to any players who continue is up to you - I think there's benefit in that. On the other hand, they did give up already and that aught to be acknowledged)
2. Have a secondary optional goal they can move onto. They don't have to take it up, but it benefits them somehow (even if just in a sense of increased PC prestige!). This goes by rule #1 as well, as they can just let it go. If really concerned you could make a third optional goal, probably the second is enough to fill out the extra session time (if filling out that time is a concern).