At present, it is not feasible to upgrade tex4ht. There has been no new full release since Eitan's death; still a work in progress.
A few runtime files have been updated in TeX Live, so if you're using TL, you can get those with tlmgr update. I don't know if MiKTeX has picked up the same fixes.
For the upstream tex4ht source repository where the work is being done now, see the tex4ht home page.