Judging from that picture there, it really looks like a dead pixel, thus a dead line. If you didn’t know, the VB has a resolution of 224×1 and makes it into a 384×224 by using the mirrors.
Only way to fix this, is to replace the display completely unfortunately. I have seen a few cases with this, but that it is very rare. Seen about 4 in a 1000 displays.
Can this phenomenon also be just a part of one line? On mine I sometimes have the feeling that in the middle of the left display a see a small “scratch” of blackness, mostly when the game is very bright and on scenes with lots of red (like on Mario Clash in the opening movie with the clouds).
This happens a lot on Gameboy’s (original and Pockets). An odd trick that can fix it (at least temporarily) is turning the system on, remove 1 battery, and put the battery back in, all while the system is turned on. It sounds dumb but its worked for me.