Hyperspace travel has its limitations, and those limitations directly affect the difficulties in surviving an ongoing chase through it.
Hyperspace: limitations and difficulties
Hyperspace: how it works (more or less)
“But the stars that marked our starting fall away.
We must go deeper into greater pain,
for it is not permitted that we stay.”
Those who have glimpsed the sub-space realm known as “hyperspace” for themselves have not taken the experience well. The earliest experimenters with the technology peered through portholes to see for themselves what the external cameras only revealed as a kaleidoscopic blur, and for their curiosity were afflicted with madness.