Binding Post Loose tweeter connection.

Out of warranty?  

First determine where is the break? The terminals you are seeing are the outer part connecting through the driver frame to wires inside that connect to the voice coil. A common modders trick is to bypass that connection and solder directly to the wires inside. So don't just fix your problem, modify it to be better. 

Rocket94,
do your terminals look like the ones in this link?

https://www.ukaudiomart.com/details/649448539-paradigm-studio-10-v5/images/1933995/

When you say you put a tight rubber band around both wire connections are you referring to the upper +/- binding posts?

it looks like you can unscrew the back plate that the terminals are mounted in to gain access to the wiring inside that feeds the crossover. Commonly used on the rear of the binding posts are collar nuts to lock down the post.  If one of the binding posts is bent visually you might be able to unscrew the collar nut allowing you to pull that post out of the rear panel and check for a fractured binding post or a loose wire connection to the post.  If the crossover is affixed to the terminal cup then there may be a broken solder joint from post to crossover board, which could explain you putting tension on the post and it making contact again.  This scenario would involve soldering skill to correct.  Pic in link of board affixed to cup.

https://www.canuckaudiomart.com/details/649510789-paradigm-studio-and-signature-drivers/images/22088...


You can take a picture of it and post it in the systems page here and then link it in this thread for members to see what’s up.

Bryhifi.

Yes, that is exactly what it looks like. May I use your picture?

A better side view of how Paradigm has done crossover board to terminal cup interfaces on many of their speakers.  You can see the area in the pics that the post drops through and make a fragile connection.  
https://www.ebay.com/itm/313336963217?chn=ps&norover=1&mkevt=1&mkrid=711-117182-37290-0&...

Not mine so feel free…I just searched for your model to see what it was like. 

Also check the post straps that run between posts to bridge positives and negatives for contact or fractures. Seen those be an issue as well. If the post is bent far enough you might not make contact when screwing the post nut down. This you can test by taking a short piece of wire to jump the lower to upper of the same polarity.
What cable connection are you using? Spade, banana or bare?

Thanks for all of this information. I bet you have the answer.

I was using Acoustic Zen Satori's with banana. I don't use these speakers anymore. I was going to set up a kitchen system and use them at some point.

Sounds sick fix it asap!!

File a claim for damage, if you can. Never except anything that shows signs of damage as that could mean there are other potential failures waiting to happen. If you're going to fix it, expect other problems down the line. Good luck!