You do not need new soil. You may have to fertilize. I use rotted leaf duff for my potting soil and use sterile urine for plant food. The plants did very well and were very productive. .

Click on the link below for picture of pepper plants and their containers.

Here is a link that might be useful:

Definitely fertilize! Not sure about your growing zone as far as time to have a second batch grow in. I hope you get them! :)