Montage some of the less important moments.
I've had some experience with long travel moments through dangerous territories in my games where originally I was having the players play out the encounters. However, after about 2-3 sessions I realised that these encounters, or fluff, were taking up way too much time and the players weren't enjoying it.
What I ended up doing was narrating these encounters, or their travel in general, rather than have it play out in game. This saved much more time, allowed the players to actually reach their destinations and begin to play out the actual relevant story parts.
Instead of having them roll to find the Sith, walk there, roll attacks as he flees, and then have them watch as he runs, narrate parts of it instead. An example of this could be:
Over the course of the next week you guys manage to locate the Sith lord again on Korriban. You carefully tracked him to his hideout there only managing to catch a glimpse of him boarding his ship and escaping.
Depending on how much the players enjoy this type of game, you may even want to reduce this chase scene down even more by narrating something like this:
After chasing the Sith lord for 2 weeks, from planet to planet, the Sith always just managed to escape even when it seemed that you have succeeded in cornering them. Finally (at the end of that month long period) you have managed to track them to ...
From here have the players play out the final showdown with your Sith lord BBEG.
Allow the players to play out these scenarios, but if it is possible for them to capture them now, allow it to happen.
I am a fan of allowing the players to decide the story. By setting a hard month time period where the players are unable to capture their enemy, as every time they escape because plot armour, is not fun for all players. Some players may enjoy being more immersed in the story, though some players may prefer to only be guided by the story.
One option is to allow your players to play out these encounters, but reward them if they come up with a good plan or succeed in capturing the Sith before your month time period is up. If you really want it to come down to the wire, I would go with my first option. Otherwise if you are okay with allowing your story to change, let the characters succeed if that is how it plays out.