Ah, OK. I finally figured out the problem. I defined the page ID for the English version on the Swedish page.
Hm, I already tried having that option on an off, but it didn’t make any difference.
There is one very important thing I forgot to mention – since I began working with the polylang plugin for this website, there has been two updates for the plugin. At first, I had this problem. After the first update, it worked as it was supposed to work. But after the second update it stopped working again.