Toyota - Sienna :: 2010 - Alarm Keeps Going Off Randomly

My 2010 Toyota Sienna alarm keeps going off randomly...there is no method to the madness. It happens after it's been running or not. It happens at all hours of the day and night. It can happen four times in a row and then not for days on end. It's literally driving me insane. I can stop it by pressing the unlock button on the remote. But it will often -- though not always -- do it a few more times after that. So, I open all the doors/trunk remotely and that usually puts an end to it for that period...but not always. But it always happens again...whether it's the next day or seven days later. The mechanic says they need to keep the car and hear/see it happen...but that means leaving my car with them for days on end, which I simply can't afford to do.