You could try strengthening your arches by doing appropriate exercise. Running barefoot does this (I run barefoot because it feels nice, but I noticed an increase in foot strength too). Start very slowly if you go that route; no more than a few minutes of running per day at first.

I'm sure the internet has more ideas in case you're not into running.

As with any of these types of issues it'll take dedication to fix, but if you truly can't stand for more than a few minutes the benefits should more than make up for that.