This error is mostly caused by the Forefront Identity Manager Password Reset Client Service (FIMPasswordReset) service not being started. This can be easily remedied by starting the service. However, if you have verified that the service is running on the workstation you are trying to do the reset from, there could be a problem with the IE zone and protected mode setting for the Local Intranet Zone.
Please note that you need to make sure that the site is running under a "Local Intranet" zone and that Protected mode is switched OFF.
A configuration as shown below will cause the error as the ActiveX component cannot check the service status if incorrectly configured, and generates the error in question.