Can I work part-time on working visa?

As for now, I'm working in japanese company on contract, but due some reasons it is possible that I would have to be demoted to part-time or arubaito (so I will work less hours and only when they need me to). Will it be legal for me, if my visa status not changed and work field is still the same? Or should I begin searching for new job and refuse of this proposal?

So currently you are a full-time contract worker, and the employer might want to change that to part-time or even to"only when needed" basis, doing the same work but less (and/or) not at predetermined hours?

That spells trouble - will you be able to live on part-time income only? Or even worse, on an as needed basis?

Even if you are ok with it now, which I doubt, you will need to report this significant change in employment to immigration within two weeks; I don't know what they will say. Also if the pay gets significantly lower, you will not be able to renew the resident status (I don't know how much lower it will be though...)