However, there really isn't anything to "convert"; your existing On Demand instance stays running and you simply purchase a Reserved Instance inside the same Zone (this part is important, see below). It's entirely a billing thing and Amazon handles this seamlessly.
[...] the conversion of an on-demand instance to a reserved instance is purely a billing issue. Simply buy a reserved instance, and the instances will be billed as reserved instance. No changes need to be made to your AutoScaling group.
Please note that reserved instances currently need to be purchased for a specific AZ. In order to get the benefit of reserved instance pricing, your AutoScaling group should be configured to launch instances in those AZs.
For example, if you only buy a reserved instance in us-east-1a, you should setup your AutoScaling group to launch instances in us-east-1a. If your AutoScaling group is configured to launch instances in us-east-1a and us-east-1b, and AutoScaling launches an instance in us-east-1b, it will be billed as an on-demand instance unless you also buy a reserved instance in us-east-1b. (source)