Oxygen woes

I have spent HOURS upon HOURS on the phone trying to get us a pediatric oxygen concentrator that runs continuously at 1/2 a liter with an extra battery pack.  Yes, it's a mouthful but it should NOT be this impossible.  We have not been able to come to a solution.  The only option that we have been given is renting one for around $400, this is problematic since we will need it over and over again.  The other option is buying...