Your texture file could be damaged...
Thanks Mylenium for your reply,
It can't be the case that my texture file is damaged, because when I make a change to the model (and because of that the model has to be rerendered), the texture gets back in place. If it turns out that it is a damaged texture file, how can I replace it without too much of a hassle?
Edit: So I found out how to replace the texture. After replacing, the problem stays. I also tried removing the texture. When I do a render without texture, the whole square (not the whole image) becomes grey, instead of just a small box in the corner.
Problem partly solved. I started my project with a huge image which I cut into pieces. Since the dimensions were more than 3000 pixels in both directions, I thought my laptop would never be able to render it, so I scaled the 300 ppi image down to 72 ppi, making the size somewhere around 900 pixels. When I render this, I get the grey box. When I do a single pass on the original image, there's no such box. Is this a bug in the software or is it just impossible to scale down this much and still be able to render a normal image?