The top sites I've had for quite a while all remain. However, I can't get a new top site to stay even though it is designated permanent with the blue pin. Here's what happens:

1. At the desired site, in the smart search field, I click and hold the plus sign on the left.
2. I choose Add to Top Sites.
3. The site is added to top sites, in the top left position, with the blue pin already chosen.
4. I drag and drop the new site to a different position.
5. The new top site will be gone next time I open Safari

I have tried toggling the blue pin off, then back on...but it doesn't help.
I made sure that the bottom right top site (that will get bumped out of top sites) has the blue pin toggled off...but no relief.

Colour me puzzled.

Clear Safari caches? Restart computer between attempts?

It sounds like it might be a caching issue to me.....

Nope. Just put the desired site into top sites, cleared the Safari caches and completed a restart. The new site was gone.

Any chance this could be a corrupted Plist issue?

This kind of behavior is often the result of a corrupted preference file. In this case it would be in your home folder Library/Preferences/com.apple.safari.plist

If you have Time Machine backups and can positively remember a time when the problem did not exist you could try restoring the plist restore the preference file from there and see if that fixes the problem. That way you won't lose any of your other preference settings.

I wasn't dealing with this issue for a few days but have returned to it.

My Safari preference file seems to be hiding. If I use "Go" from the menu bar in Finder and choose "Home", I go to the User (me) but there is no Library folder. If I travel HD/Library/Preferences, there isn't a Safari plist. The plists go from com.apple.print.makequeues.plist to com.apple.screensaver.

FYI, since these posts I have upgraded to High Sierra from Sierra, in case that makes a difference. Does it keep some files invisible?

The user Library is hidden by default in Sierra and High Sierra. You can overcome this easily, however. Read How-To Show Your User Library in macOS High Sierra and Sierra. There is a Safari folder within ~/Library and you may be able to locate the relevant preference file there.

Good...thanks for the link. Interesting site.