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?