Just in case anyone else is interested in this, I contacted Lenovo who replied saying "The production versions of all the apps are ONLY on www.lenovo.com/shareit
I had by then uninstalled and re-installed another copy from this main Lenovo site, and this copy was working fine.
I had installed the first non-working copy from kc.lenovo.com, which was pointed to by several Google results, and referred to it as the stable Windows version. I have no idea whether this is an official Lenovo site, but it is confusing.
The reason for my extensive installation is that I work primarily with audio and found ShareIt extremely useful for moving files between computers and tablets quickly and easily.