Does anyone have an infant that was born with arm paralysis?

Transient vs long tm. The forces that occur in the moments of a delivery can place traction on nerves that come out of the neck & supply the arm.It is relatively common for arm to be limp for a while due to swelling around the nerves.Onset may be immediate or later after swelling occurs, most swelling subsides in a day or two & function returns.Some kids need therapy to recover, rare cases can be permanent.
May be Erb's palsy. Your question is a bit vague but if the infant has only one arm that is not moving and otherwise doing well. It is possible that he/she is suffering from a brachial plexus injur (called erb's palsy). This is a very complex subject and can be further read at ; http://orthoinfo.Aaos.Org/topic.Cfm?Topic=a00077.