So, I have found the following:
The BitBtns that are newly created in Lazarus 4.8 work without any issues.
However, BitBtns that come from a Lazarus 4.6 project lose their glyph in Lazarus 4.8 when the project is closed and reopened (although, strangely enough, this does not always happen). After compiling, however, the glyph is always missing from the application.
I have attached the project. The glyphs I use are 32x32 pixels. Screenshots showing my systems are included in the attached ZIP file.