I'm sorry to hear about Roxie's cough. It sounds like you have tried a lot to get her better- she's lucky to have you looking out for her.
There are a few things that come to mind with a chronic cough in an older small breed Pomeranian mix. The first would be tracheal collapse. Sometimes we are lucky enough to catch this problem on an x-ray- but most of the time we are not. This is because the trachea is not in a constant state of collapse- it is a dynamic process, and often collapses during the expiration phase of taking a breath- so it is not easy to catch at the right moment. If you are willing to take her to a specialty hospital for further diagnostics, they may be able to do a more advanced imaging test called fluoroscopy- which is like a "live" x-ray. Many cases of tracheal collapse respond well to steroids- which you have already tried. The steroids are the key with managing tracheal collapse, but some cases also require a strong cough suppressant in addition to the steroid (I often use butorphanol as well). These medications are continued life-long, at the lowest effective dose, in order to manage the cough. There are more severe cases, where medications will not control the cough, and a stent can be surgically placed within the trachea to keep it open.
Another possibility is chronic bronchitis (asthma). Usually there are changes seen on the x-rays that may indicate bronchitis. This too, is managed with steroids, and often antibiotics when needed.
The third thing I can think of, that could be a cause of chronic cough is a parasite in the lungs. This is less likely, but with any pet with a chronic cough- I always give a course of dewormer- usually 10 days of fenbendazole- just in case it has a parasitic cause. It can be difficult to diagnose lung parasites- but a test called fecal Baermann may help with diagnosis.
My recommendation at this point would be to consider a few different options- 1. taking to a specialist for more advanced testing 2. taking to another veterinarian for a 2nd opinion, or 3. talking with your current veterinarian about trying another course of steroids, with a cough suppressant such as butorphanol tablets, and possible the course of dewormer as I mentioned.
I hope this has helped, please provide a rating for me.