Incumbent leverage
If you're a 1099 and the contract is coming to an end, you have an advantage on the re-compete because you are an "incumbent" for your position.
They are going to want to retain you for the re-compete so this is a good time to exercise some of your leverage.
If you want to stay on the project I'd advocate for a higher bill rate and/or a higher LCAT.
If you want to jump somewhere else on the contract, you could ask that they submit you for other positions.
If you want to grow a biz, you could ask them sponsor your Facility Clearance if you don't have one and/or ask for a few guaranteed spots to fill if you do have one.
Remember, you can both help each other so you're not offending anyone.
You are advocating for yourself and in exchange, you give them a higher chance of winning the re-compete.
Learning to recognize when you have leverage, and knowing how to use it, is a critical skill as a 1099 (or even as a W2). This is how you become a 1099 in the first place, and how you get better rates, schedules, projects, etc.
Want the full playbook? Check out Going 1099.