That sounds like a problem with the printer to me. If the image looks ok in Inkscape, there's not much we can do.
I don't know, maybe someone here knows something about printers, and could help. I'm not sure what to say.
Are you sending it to the printer directly from Inkscape? If so, you could try saving the image as PDF, then open it in a PDF reader, and print from there. Maybe that would work better?
Or I guess maybe if the lines are all very thin, the printer can't read them very well?