I have tried out two things to solve the display issue yesterday and today, but neither of them have made any difference:
(1) I replaced the "problematic" entry properties folder on my server with a copy from the current version of s9y that I uploaded from my PC, just in case the server version had somehow got damaged; and
(2) I got s9y to verify the correctness of the installation from the Maintenance section of the admin interface (everything was verified as being correct). I'm using Serendipity 2.1.1.
I am not a programmer and have not changed any of the PHP files. I can't say what's wrong. Yellowled has implied it may be to do with the current PHP version, which may be the case, but doesn't really add up as v 5.5.38 is not the latest version of it available.
I now realise what I initially said about the blog not being displayed in certain browsers actually applies to every browser with an empty cache; the "correct" versions of the blog I've been seeing were simply (and deceptively) cached data. Which means that any new visitors to the blog will have been seeing something different: an error message.
I'll ask my web host about the issue today and see what they say as they recently upgraded the PHP versions in use on the server. Perhaps that will lead to some new insights. But I doubt it.