If you haven't been charged and arraigned you should not be on house arrest. You may be on the pre-trial services program where you are out under restriction in lieu of detention and bail?
Generally speaking, and without more facts to base the response upon, you can remain in that situation for the entire length of your speedy trial time. Speedy trial is 90 days for a misdemeanor and 175 days for a felony. These time periods begin to run the day you are first arrested and say you are entitled to a trial within the time. If never arraigned, or formerly charged, within that time, the periods accrue anyway and charges afterward would effectively deny you a speedy trial. The speedy trial expiration defense would have to be raised however. If no one objects to expiration of speedy, your case would likely proceed.
What you are probably referring to is the pre trial release program known as "ankle monitoring", or some other version of it. "House arrest" usually refers to a sentence, once the case is over.
The arraignment dates usually gets continued a few times. This is becasue the state generally has 41 days to file formal charges on felonies, for those incarcerated. Longer if you are truly released from any "restrictions" or constraints on your liberty. So the court date will come, it is just a matter of when.