The revelation of the Halting Hex in Jessica's possession threw the entire house into a frenzy, but the announcement may not have had its intended effect. This accepted temptation could not only prevent Jess and Cody from being evicted, but also completely waste a week of gameplay for the HOH. But Paul is currently the HOH, and there's no way he's going down without a fight. Since learning about her power, Pau's been trying to convince Jessica to not use Big Brother's Halting Hex. However, this seems to be the only predicament that Paul can't talk his way out of.
The reasoning Paul gives Jessica for not using the Halting Hex actually makes sense. If Jessica uses it this week, she can't use it in the future. If she managed to pull herself off the block and throw Cody to the wolves, then she could still be in the game and save the Hex for a week where she desperately needs it. While Paul has succeeded in planting seeds of doubt in other relationships, the bond that Jess and Cody have is too strong for him to break. Jessica realizes that they are both on the bottom of the totem pole, and without each other they have no one.
Jessica is afraid of losing Cody, but aligning with Cody hasn't exactly been great for her game. The week before Paul tried to break them apart, Jessica trusted Cody instead of her gut and made a major mistake. They both wanted to evict Josh, but Cody told Jessica to not use the Power of Veto and leave Ramses on the block as a pawn. Sure enough, Ramses went home. Cody staying in the house may provide Jessica with a trusted partner in the game, but if he's going to be giving her counsel then he needs to get much better at playing Big Brother.
Jessica explained that despite issues in the past with Cody, she feels that using the Hex to skip eliminations this week is the only way to ensure that she'll be able to play to the best of her ability. From Jessica's point of view, the biggest reason she's using the Hex is that there is no one else in the house that she could turn to for support. As she pointed out to Paul on the live feeds:
Cody may not be great for Jessica's game, but his flawed counsel is far better than having no one to talk to. Jessica has already felt the loneliness of not having Cody in the house, and she's not interested in going through that again. Using the Halting Hex may not be the best long-term plan for Jessica, but if she doesn't use it there may not be a long-term to consider.