Toyota mr2 2001 Power steering goes on and off.. what could be wrong ?

it's broken get it serviced

If you are saying the steering is difficult to turn you could have a blocked hose or a problem in the gearbox.
Or something in the front suspension such as a faulty ball joint.

You MUST have the power steering flushed and the correct fluid installed, failure to do this right away can result in permanent damage to the power steering components

the idle sensor on the powersterring pump is weak or your low on power steering fluid

thats a complex job that if goes wrong it goes very wrong so my advice is to go to a garage

change the powersteering pump. It sounds like it is burnt out.

It sounds like your power steering pump has gone out. If your resevoir has fluid and there are no power steering lines with holes in them, that would be the next option to look at. When the pump goes out the fluid cannot move throughout the tube to help give you assitance in steering. Change this pump and your power steering will be back to normal. Please let me know if you have any further questions. Thanks for using FixYa!

I don't know about hybrids, but on most vechiles, you check power steering fluid with engine running.

I just found 1 of my power steering leaks in my 1990 toy pickup. My high pressure line has a hole in it. I used a florecent die kit to locate the leak. You can get it at Autozone.