I didn't think the Coagucheck was available for private use in the US right now. Or did that recently change again?
Some insurance companies want you to be on Coumadin for 3 months, or as along as a year, before agreeing to a home testing machine. Other insurance companies require that they see an out of the ordinary need, such as distance from lab, unstable INR or some such thing. If that's the case, and your doctor is agreeable, they can stretch the truth for you.
Don't give up. How did you apply for the machine, did you do it yourself or did you use a company like QAS as a go-between?