Sounds like you have discovered a game- or level- design issue which you might want to address in other ways, such as reconsidering how the game rewards success, or shifting to an alternate game mode where there is a secondary goal when the main goal will no longer be possible. The details depend on the game, of course, the expected players' interests, and what you want to accomplish. But having some early mistake mean there's no point in continuing can be an annoyance for some players, depending on their expectations and how it's presented.
It doesn't have to be a bad thing. For example, if your players are perfectionists and want to practice something over and over till they get it right. Perhaps in many Olympic sports, the point is to have the best performance among experts, so if you stumble at some point, you might as well stop trying for that round, and that's expected. In that case, it may make sense to indicate when winning or proceeding becomes impossible.
Or, if it's a puzzle genre where again the expectation is you'll probably make mistakes as part of learning and need to start over, but part of the game is figuring out what to learn from mistakes, then you may not want to let them know, so they can figure it out. Or you might want to let them know, but in a relevant and interesting way that provides a clue to the mystery they are supposed to figure out.
In games where there is rich gameplay aside from the main goal, you may not want to announce a hopeless condition, because trying to continue play can be interesting in other ways.
In games with more going on outside the current mission context, or where you want to have it be fun even when things go wrong, you might want to detect failure states but instead of announcing it like a failure and suggesting trying over, you could have the gameplay respond or give clues that the player should now be focusing on some secondary or alternative goal. For example, if the main mission were to accomplish something without something happen, and that main goal becomes impossible or failed, you could let them know that (or not) but have the situation change or a new goal become apparent. For example, if you were trying to rescue someone from someplace but that becomes impossible, your next goal might be to not get caught yourself, and might be signaled by a companion or observer character pointing out the situation, or an alarm going off, or several guards showing up.
The above can even apply to a game with one-minute levels, and is a design decision. If you just have them stop and try over, that will have a certain flavor. If you have there be a secondary play mode, that could have another flavor. For example, if you can't win the current level, you might still be able to escape with your life, and/or gain some secondary points or power ups or cause some effects that would carry over to the next try.