A couple of experiences of mixed success.
I rebuilt some planters for my Grandma a few years back that were to low (a friend of hers had built her some but they were only 6" deep and were always dried out and were hard for her to reach). She's not a in wheel chair but she is 90 and has a pretty bad back so bending over to weed wasn't working and there was the not growing well/moisture problem. I just built these out of 2x12s screwed into 2x2's at the corners they are a smidge over 24" high which was right at a handy height for her to sit in a chair next to them and weed. The specific height would imho be mostly driven by the needs of the person. At 24" they had plenty of dirt for pretty much any vegetable and grew some swell tomatoes over the last couple of years (and a nice little herb and flower garden in the other one).
On our deck I'd re-used some cedar boards from the fence I put in for the dogs when we moved in here and made some 12" deep by 18" wide planters and put them on our deck. I eventually gave up on them for a couple of reasons. The 12" depth with the thin fence boards wasn't enough to maintain a reasonable moisture content very easily (more on that later). We have a real lack of sunlight on most of the deck so it was hard to get much to grow real well a lot of the time. Having said that we got some good peas out of them and some greens did pretty ok. A couple of them I put up on small saw horses for accessibility and those had even worse moisture control problems. The other ones I'd raised on 2x4's to avoid rotting the deck out under them (worked) but they still dried out pretty fast. The planters at Grams house are right on the ground next to her deck and have thicker walls so less problems there. The ones I had here eventually moved to a friends house where they're living out their remaining years as flower planters alongside their patio and are working pretty well for that.
This isn't to say you can't get it right with a raised planter, just that its a bit harder and you have to fuss with the soil mix and moisture management a bit more to make sure it doesn't end up to wet or to dry all the time compared to a deeper one sitting right on the ground.
From these experiences I'd say that 12" is the absolute minimum I'd make the soil box of a planter unless you have a LOT of time to fuss with it every day and are willing to forgo some of the deeper rooted veggies.
I'm not sure about the accessibility issues from the wheelchair, it might be worth doing a cardboard mock up to make sure they can easily reach everything?
Also note that unless you're the hulk you ain't lifting a planter of any size once its full - even if that was the plan.. and its on saw horses
Sorry I don't have any pics of either of them.
Ted: I like the looks of some of the planters in the tenten link