A central theme of RPGs is that characters will often fail at tasks. For some situations failure is not too terrible. If you can't pick a lock just consider your PGMP-12 a very noisy lock pick. If you have to climb that cliff face and you miss a roll you try again. You were using ropes and pitons and all that survivalist stuff, right?
An important consideration is whether a referee allows a character to attempt a task again after failure. Obviously it's a good idea if that failure is going to result in a total party kill or a campaign going off the rails. It's equally obvious that characters need some kind of penalty for failure. Otherwise they'll keep retrying tasks till crack of doom or the pizza runs out.
Ct already has a system you can apply to retrying tasks. Swinging a blade in combat is pretty straight forward but it is a task. Each swing however costs you a point of Endurance. When your tank is empty you take a -2. Why not apply the same principle to tasks? So repairing that bearing on the main engine before your Scout ship falls into a gas giant takes an endurance point per attempt. Retries or too many tasks at once will tire out the technician. Bear in mind that if you're fixing stuff in the middle of space combat a character will regain a point of endurance every 2 or 3 turns depending on the system and scale you use. The length of time for a task can usually be inferred from rules or real life (if you don't own an air/raft use the rules.)
For truly epic jobs a task could be broken up into two or more die rolls (each taking a point of Endurance). An EVA repair job immediately springs to mind. Going by the experiences of the ISS crew those things take a while (and are hard on the fingernails). You might even penalize a character for wearing a low tech space suit for example or other uncomfortable work conditions.
What happens when your Endurance runs out would depend on the task. At the very least the character would be subject to a large minus for anymore attempts (-2 to -4). The referee might disallow any further attempts until the character has rested and regained some Endurance. He could also rule that a failure at tasks you attempt with a minus results in some mishap.
This is not the sort of rule you use for every roll a character makes. But by the same token using Endurance to fuel rolls could simulate some difficult non-combat missions; EVA repairs, asteroid mining, working out jump coordinates with that enemy cruiser bearing down on you, forced marches or difficult climbs. Now characters working against a clock will also have to deal with their own fatigue. Do they press on or do they take a rest? Do they wait or take a chance on blowing the job?