In Trek the phrase "full impulse" might really mean no more than about twenty percent of light because with warp drive you don't need to deal with relativistic complications. It doesn't mean the ship can't get to ninety percent of light, but that there's no point to it. And at twenty percent light the time dilation effect is minimal.
So the Enterprise
probably could use her impulse engines to get up to ninety or ninety-five percent light to get to a near base, but the penalty in time dilation makes it costly. Now if the ship hadn't been able to re-energize the warp engines then they might have gone for it, but until they knew for sure the engines couldn't be repaired then they wouldn't bother trying.
They still might have experienced some measure of relativistic effect if they'd pushed the impulse engines to get to Delta Vega. I don't have the hard math with me, but at ninety percent light Delta Vega may indeed be only a few days away for them while still distinctly longer in the objective sense.