Unfortunately, this is one of those questions that should be answered by a medical expert - not only does an adequate dose of prednisone (or any medication) vary from person to person, but I'm simply not qualified to say.
What I can tell you, though, is that many rheumatologists will prescribe a dose of prednisone along with other DMARDs (methotrexate, Plaquenil, the Biologics). This one varies from doctor to doctor, as well. Some won't give you any prednisone at all, except in emergencies or control the flair and the others consider it a safe practice to include it as part of your regular meds. Prednisone can give it a wonderful boost to meds and to your well-being in general, but like any other medications, you have to consider the pros and cons, risks and benefits and what you can do to manage those risks (e.g., we'll have a post up tomorrow about osteoporosis).
Have a conversation with your doctor about this. The main issue is that through getting prednisone for your asthma attack, you've discovered that the medications you are currently taking are not managing your RA and/or pain levels properly. Does that mean you should consider prednisone on regular basis? Maybe. However, it may also mean that you and your doctor me to take a look at your current medications and whether you need to increase the dose, add another of the DMARDs or switch altogether. It may also mean that you are not getting adequate pain control, so if your rheumatologist is not comfortable prescribing pain meds - and many aren't, although I cannot imagine why, as they specialize in a disease that comes with chronic pain, but that's a rant for another day - where was I? Oh yes, ask for a referral to a pain specialist.
Please let us know how it goes?