There is no law determining the length of time a private company must keep its surveillance video. That particular Target may keep the video for 1 month, 3 months, or the video may just continuously tape over itself every few days. It depends on the system that store is using and the policies in place. You could call that Target store and ask to speak to a manager.
You should probably call Visa or your bank first. You may have certain protections offered by Visa or your bank in the event of theft. Usually, if you have these protections, the bank will refund you the money without a lot of questions as long as your claim is less than $1000 and you have not made too many claims. Simply explain your situation and ask what their claims procedure is.
You can report this incident to your local police and they may investigate the theft.
What are you waiting for? Fill out a police report. Yes, there is a chance the police can catch the person. Don't talk yourself into not doing it.
Clifford L Tuttle, Jr
Attorney at Law