Were you a new employee signing up for benefits in August? I don't understand why you would sign up in August and then again in December. That question number one. Question number two would be it would be knowingly they withdrew the money because you authorized them to in September. They didn't for October, November and December. That is odd. You definitely need to address this with HR.
STD is used for pregnancy. The theory is that you are disabled during the 6 to 8 weeks. If you want additional time, and depending of the size of your company you could be eligible for FMLA which is not paid.
In our company, STD is paid by the employer. So there is no "signing up". It is also based on your length of service. For example, if you have been employed three years, you get one month at 100% pay, one month at 80% pay and one month at 60%. Then you are done.
Contact HR ASAP. Discuss it with them, don't yell and scream. I'm in HR and there is nothing worse than that.
You need to check your pay stub ALL THE TIME. While it was an oversite with payroll, you also contribute because you didn't check. I do feel like there is more to the story.