In the episode "Children of Time," we learn that in the original timeline, the Defiant was thrown back in time and crashed, and Kira died because Bashir didn't have the medical facilities on board the Defiant to treat her. So the second time around, the choice presented is that either the Defiant avoids the crash and all the inhabitants of the planet cease to exist, or Kira dies once again. Question: Since the crew now knows about the anomaly and how to avoid it, and since Kira originally died and therefore didn't matter to the timeline of the planet, why couldn't they have just put Kira in a runabout or shuttle and let her head home safely, while the rest of the crew went through the anomaly so that the inhabitants of the planet would survive?
It really seemed to me to be a plot convenience to provide the alter Odo with an incentive to destroy the alternate timeline to prove his love for Kira. Not to mention since the technobabble whatever field that made the Defiant crash, how would a shuttle get through it? They don't have super anti-technobabble deflectors like the main ships do.
In addition to the comments already made, there is also the matter of Kira's absence affecting the timeline, as it's likely someone else would have taken her station on the Defiant bridge in the event that she used a shuttle to return to the station. Even a relatively minor change can have significant repercussions.
The answer is... Because the writers didn't think about it. The Defiant is equipped with the Chaffee, a warp-capable shuttlecraft. During the episode, O'Brien easily is able to launch a class-four probe through the barrier with no problem, and a class four probe doesn't have nearly the shields of a shuttle or runabout. Kira could have hopped in the Chaffee, gotten to the station, gotten fixed and been back in time to snuggle with Old-Man-Odo without a second thought. But we have to remember that the writers are human and wrote these episodes under extreme duress and time constraints. You can't expect them to remember everything, like that the Defiant had a SHUTTLE, yes?
To quote James Cameron, "The script says Jack dies.He has to die." Had the various alternatives been explored deeply or pointed out to the writers, they would have put together a string of technobabble that would have made Kira's independent salvation impossible. The shuttle would be too weak. Too many crewmembers would need to go with her. Etc.
" The shuttle would be too weak." And yet a class four probe would make it just fine? " Too many crewmembers would need to go with her. Etc." It's a simple warp-capable shuttle. Nobody but her needs to go on it. Like I said before- it's only because the writers didn't think about it. It's the same reason why they continually forget about how casually Kirk flitted back and forth through time in TOS- because then you wouldn't have a show.
Dax: Chief, if we reconfigure the [emitter name] on a class [number] shuttle, can Kira make it through the energy barrier on her own. O'Brien: Maybe. But in order for it to work, I'd have to remove the positron [equipment name] from the Defiant and attach it to the shuttle's warp [gadget]. Sisko: But Chief, the Defiant's graviton [emitter] is designed to operate on a subspace [wave type] of 18 [frequency measurement]. O'Brien: True. [long pause] But in order to do that, I'd have to [techno] the [gadget] conduit to the main ODL [scientific adjective] shunt. In order to do that, I'd need a [particle name] capacitor. I left my one the station when I realigned the [gadget] on upper pylon two last week. Dax: We might be able to make one if we reconfigure a flux [tool name]. O'Brien: Yes, but if it's off by two [quantum measurement], Kira's head might explode like an [planet name, adjective form] [animal name]. I wouldn't want to be blamed for that. Sisko: Then you better get to work! [After a brief montage] O'Brien: That's it. We burned out the [gobbledigook]. This shuttle will never fly again! That's pretty much the dialogue that would have "fixed" the episode, the same dialogue that appeared in every Berman-era episode in which the technology saved the day. It would have chewed up a lot of time that could have been spent on the Defiant's crew's feelings towards the people on the planet.
But then... how did a simple class four probe so easily get through the barrier? The writers damned themselves with that little bit.