You might have to narrow this question down to a specific location and a specific problem.  The shots are supposedly mostly local, not systemic, so should not have the long-term effects of oral or IV prednisone.  However, local shots can still sometimes do local damage.  I had several cortisone shots in my foot for neuroma (this is not RA). Usually they don't do more than 3, because it causes atrophy of the fat pad of the foot (not good).  I believe this, because this year my neuroma became a problem again, and I had the fourth shot.  It felt much worse, like it went right to the bottom of my foot and swelled it up - though it didn't look it.  So - it's either put up with it, get a shoe change/adjustment, or consider surgery for it.  Luckily, it's tolerably compared with other problems!

   I had cortisone treatment (not shots, but iontophoresis with cortisone, because shots can cause tendons to rupture or deteriorate) on an ankle tendon.  The benefit was shortlived, and in fact I believe that it actually weakened the tendon, leading eventually to the surgery I had a year and a half ago to reconstruct the tendon, even tho, it didn't actually rupture or tear.

    In addition, I have had cortisone shots in my wrist, jaw, shoulder (several times, well spaced), and once in a trigger point on my upper back.  All of them were helpful, with no negative effects (that I know of, anyway!)

     Some people with RA for a long time that can't take stronger meds have repeated series of cortison shots in their joints.  I think that's less common now, with all the other meds, and I think the benefit may wear off at some point, but I can't really comment on it for sure.

    So you see - your question is very general and the answer needs to be to a more specific question. Perhaps if you can tell us what you're refering to as the problem, you'll hear from someone with a similar problem...

    Wishing you well -