Doctor Who, particularly the revised series, talks quite a lot about "fixed points in time". These are events that are set in stone, and for whatever reason, can't be changed. One of the gifts of being a Time Lord is knowing when these are. (Preventing the death of someone seems to be a common one, for example.)
We've only seen two cases, so far, where The Doctor tries to prevent a fixed point in time from happening:
- In "Waters of Mars", he rescues the captain the Mars station, who was supposed to die. Her death was fixed partly because it would inspire future astronauts. We never see any negative effects here because she commits suicide in order to fix the timeline.
- In "The Wedding of River Song", we see a much more useful example: River prevents herself from killing The Doctor as Lake Silenco. This causes time to fracture, exactly what the Time Lords are warning about in "Hell Bent"
The key here is that River Song breaks all of time with what she did. The past, present, and future all break down at the exact moment where the fixed point was changed. We end up with Winston Churchill riding a mammoth, among other things. In addition, the damage to time seems to start out localized but spread out: the entire universe, for all of its history, seems to be at risk of being destroyed.
So, the reason Clara's death is so important is that changing such a fixed point (and we have to assume it is one, since multiple Time Lords claim it is) wouldn't just break things from that point forward. They would destroy all of time, eventually causing the universe to never have existed.
However, the other thing we have seen, repeatedly, is that time is rather flexible with it's definitions of what makes a "paradox". Going back to the "Waters of Mars" example, the fixed point in time was "broken" for several hours, at least, before it was fixed; similarly, in episodes like "Rose" we seen very long periods of time go by with no long-term negative consequences.
The way things seem to work, time is malleable enough to handle a bit of bending and stretching, as long as the damage isn't permanent. As long as Clara eventually gets back to the extraction chamber and reinserts herself into her own timeline, and death, that's enough. Because time is not the linear progression that humans imagine it to be, there's really no issue of "taking too long" to fix something. (If Clara died somewhere else, though; or for some other reason became unable to reach Gallifrey again -- that would be a different story. That would be a permanent break in time, and bad things might happen.)