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A typical dose of depo medrol for an 8-10 pound cat would be somewhere around 10-15 mg IM. I usually do not repeat it more than every 4-8 weeks.
Anytime we use steroids long term, we increase the risk of infection, pancreatitis, diabetes, among many other potential side effects. The good news is that cats seem to be a little more resistant to the bad effects than dogs and people.
Some cats with asthma respond positively to bronchodilators like theophylline. I would ask your vet about the benefits of such a medication.
Good luck and I hope this helps.