This is a problem in one of the damper-related components, most likely the switch, but it may also be the motor or the damper door.
The damper is a door inside that opens or closes depending on cooking mode. If the controller senses that the door is not in the right position, it will shut down the cook cycle.
Sharp models stop after 59 seconds.
We have the 2 service manuals needed for this model and have uploaded them to our site here to help you:
http://www.microwavedisplay.com/r1870_r1871_sm.pdf
http://www.microwavedisplay.com/r1850_sm.pdf
You will need the free Adobe Reader to view or print them. You can download that here: http://www.adobe.com/products/acrobat/readstep2.html
The best place to order Sharp parts is Tritronics at http://www.wehaveparts.com
Good luck and be safe.
William E. Miller
prototech@usa.net
http://www.microwavedisplay.com
William Miller
August 2008