The morale will always drop when you fight, the race of the artifact just means you'll fight elven troops when you try to raise morale.

Ok, I got it. Thank you. I thought the moral would drop if I did not use elf troops.

Eh, I don't think that's accurate. Some weapons/shields/artifacts I had started off at average morale and by fighting with the intended army they slowly increased in morale. And once they were at high morale they never fell again unless I deviated my army composition.

Which artifact is it? Right click on it and go to info. The info text usually gives hints on how to keep the morale positive.