Follow-up to Rena's post: well, "kept unchanged" certainly occurs, e.g. In scientific writing: "we studied the cells' behavior for different concentrations of calcium, keeping all other parameters unchanged (while all other parameters were kept unchanged) or the like.
Outside of this context, "keeping all other parameters the same" would be preferable (simpler). Stay unchanged is rare, indeed, but not wrong ... The doctors tried everything they could but his condition stayed unchanged ... hm, I'm itching to say "stayed the same" or "remained unchanged" here, but I don't think the first version would be wrong.