Depending on the scenario / setting of your game, the following things could work:

Note: Those are just some quick ideas and not completely thought through!

1. Perhaps you can weave in something like the following into the narrative: "Your hacker computer is having hardware issues since a few hours ago. It will only keep running for a certain time, before overheating. So be fast and stay away from brute force methods that stress your machine and so shorten the time before it overheats".

2. If that hacking bit (at least in one of the missions) is a piece of work that lasts several days in game time (not in one session of course), there might be the risk that authorities silently recognized the attack (triggered by a high risk, high reward decision of the player) and started investigations. As a result they might be out to get you. So to put some stress on the player, you could work with sound, e.g. police sirens and which puts extra stress on the hacker, since he/she doesn't know if they are coming for him/her or just passing down the street. Some additional game element, such as hiding your hacking involvement might be implemented, so that the player (if he/she thinks he/she is about to be made by the police) can hide their involvement e.g. by deleting parts of their previous results. The in-game results could be time loss, but at the same time averting the game-over state.

3. A similar idea: If you are always hacking away from home, that won't play any role. But if for special missions you are at a special location (had to break into some backbone data center or perhaps something a bit more likely), there might be security personnel wandering about. And if you hear them or see their flashlight cones wandering around, you have to stop typing in order to not be made, which in return costs you valuable time = enhanced stress level.

Depending on the scenario / setting of your game, the following things could work:

Note: Those are just some quick ideas and not completely thought through!

1. Perhaps you can weave in something like the following into the narrative: "Your hacker computer is having hardware issues since a few hours ago. It will only keep running for a certain time, before overheating. So be fast and stay away from brute force methods that stress your machine and so shorten the time before it overheats".

2. If that hacking bit (at least in one of the missions) is a piece of work that lasts several days in game time (not in one session of course), there might be the risk that authorities silently recognized the attack (triggered by a high risk, high reward decision of the player) and started investigations. As a result they might be out to get you. So to put some stress on the player, you could work with sound, e.g. police sirens and which puts extra stress on the hacker, since he/she doesn't know if they are coming for him/her or just passing down the street. Some additional game element, such as hiding your hacking involvement might be implemented, so that the player (if he/she thinks he/she is about to be made by the police) can hide their involvement e.g. by deleting parts of their previous results. The in-game results could be time loss, but at the same time averting the game-over state.

3. A similar idea: If you are always hacking away from home, that won't play any role. But if for special missions you are at a special location (had to break into some backbone data center or perhaps something a bit more likely), there might be security personnel wandering about. And if you hear them or see their flashlight cones wandering around, you have to stop typing in order to not be made, which in return costs you valuable time = enhanced stress level.

4. In addition to my idea #2: If you hack an institution, the police would arrive physically at your location. If however, you hack another individual, more specifically another hacker, he/she might try to attack you in return, so you would have to fend of their attacks while still still keeping your own ones going as well.