Open enrollment time in which you work is the only time you can make changes to insurance deductions before taxes. This is not a rule made by your employer - is an IRS regulation (section 125) which states that you can not make changes to a plan pre - tax outside of open enrollment time . There are some exceptions to that rule, but his case is not one.
An employer has some leeway to grant the exception, but are not required to do this. Allowing you to place them dependent coverage will be out of compliance with IRS rules. Something you probably are not willing to do for you.
The only thing you can do is plead your case to your human resources department and promise not to miss deadlines .
If they say no , you will have coverage under the dependent child until the end of the year. Watch for the time periods during the next open enrollment and make sure you have other coverage for your child in a row before dropping dependent coverage .
