Which version of Acrobat are you using to combine the files?
In general, this should not happen with "good" PDF files. There are a number of problems I've seen over the years when at least one "bad" PDF file is added to the mix, where fonts and glyphs are getting corrupted. Usually, glyphs (these are the drawings of characters or character groups) disappear when you combine such files.
You may want to try the workaround that I came up with that works for some of these corruptions: Workaround for Missing Characters After Merging PDF Files
Thanks for your quick answer.
I'm using Acrobat X std., version 10.1.16. I did find an easier workaround: Instead of opening file1 and then inserting file2 into it (i.e. Tools -> Insert from File) I used File -> Create -> Combine Files into a Single PDF. Then the two files were combined without any encoding problems.
However, I am interested not only in a workaround, but also an explanation, so that I can tell the bank or their delivery mechanism to fix the problem, so that I won't have to use the workaround again and again. The bank sends the documents to a cloud service from where I download them. The bank puts the blame on the cloud service, the cloud service puts the blame on Adobe Acrobat - nobody is taking responsibility :-(
Without being able to poke around in the files, I am not able to explain exactly what is happening. When you go to the link I've posted, and then scroll down towards the end of the comments, I have an explanation for why this might be happening.
Thanks, for now it's enough for me to know that the problem is caused by one or both of the original documents.