Here's a "solution" (was Re: Apps on SD card disappear after reboot, ...)
I found a useful workaround that "solves" the problem: I installed Omni Swipe and set its "favorites" to the apps that I'd moved to the sdcard. Omni Swipe remembered them after I restarted the phone, so problem "solved." Omni Swipe isn't a desktop replacement launcher like Nova (which I tried but Nova didn't solve the problem... in fact Nova was even worse than the stock launcher, which could launch the sdcard apps in its app drawer, whereas Nova didn't even list the sdcard apps in its app drawer). Omni Swipe is a launcher that pops up when the user swipes inward from a bottom corner.
There are probably other alternatives (pop-up or desktop replacement launchers) besides Omni Swipe that will remember the user's selected "favorites" after the phone is restarted. I tried a couple of desktop replacement launchers that failed to retain sdcard apps' icons on their desktops, before I succeeded with Omni Swipe. I hope other users with the sdcard problem will test other launchers and post their results here, in case Omni Swipe contains spyware, or some alternative is smaller or better in some way.
For reference, my phone is a ZTE Midnight Pro LTE running Android 5.1.1. The app drawer of the stock Android launcher includes the apps that were moved to sdcard and can launch them and can copy their icons to its desktop, but restarting the phone removes them from the desktop. (The sdcard apps are still in the app drawer after restarting, so re-installation of the apps from Play Store isn't necessary.)