Tracheomalacia is condition where the wind pipe or the trachea has floppy muscles and flop with breathing movements. It would not respond to medicinal treatment but the good thing is it tends to get better with time, till that happens the child is likely to need support in the form of CPAP. How much time it is going to take is any body's guess! Since there is history of convulsions, I am sure doctors would have looked into the neurological status of the child to see if the difficulty in breathing is related to any brain involvement.