Please note that this is entirely based on my own experience, rather than on any medical training.
I have been taking Prednisolone on and off since my mid-teens for life-threatening asthma, but since getting the diagnosis of Ehlers Danlos last year, I have noted with interest how my joints respond to being on/off the Pred.
At the high starting dose, I find that my joints do feel a bit better, but also a little bit wobbly, as though perhaps there is swelling there, but that it keeps the joints 'held together' a bit, so they feel unstable when the Pred starts to work to reduce the inflammation.
I don't imagine that your doctor would want to keep you on a high dose for any length of time, but I find that after a few weeks, I lose strength in my core and proximal muscles (particularly around hips and shoulders) - this is a common side-effect, and that my joint stability really suffers at that point. My physio and I work really hard on those muscle groups anyway, especially when I am on steroids, but it does feel like a bit of a losing battle after a while.
I would recommend having a really open discussion with your doctor about it. I don't want to sound like a complete killjoy about it - you may find that reducing your inflammation is really beneficial over a short course, and I would think it very unlikely that you would lose much muscle tone over that time, especially if you're aware of the risk and work on preventative exercises with your physio.
Oh, and I've just thought that lots of people with hypermobility have other coexisting connective tissue/inflammatory issues, which might be very much improved by steroids, in which case it would be very much worth a shot.
Good luck with whatever you decide, and if you do decide to try it, let us know how you get on. I'm sure that you won't be the only person for whom doctors suggest Prednisolone, in which case it would be very helpful to know your experiences.
29 years old, diagnosed with EDS-H at UCH in 2009. Severe brittle asthma since childhood.