Thanks for replying, jcl.
I checked SiSoft Sandra to be 100% sure my card supports 4096x4096 textures. It does! Additionally, the texture I am using _is_ named as "cube+6.tga". It is nothing but a normal 6-sided skycube TGA which is not used on a sky entity but as a cubemap for my watershader.
Maybe this has something to do with the dx9-effects compiler because whenever I use the file as a skycube, it works and is rendered without any complaints. This is additionally strange as the texture is "only" 3072x512 pixels in size so that the card shouldn't have any problems with it even without the "+6" at the end of the filename.