Thanks for all of the suggestions. I have an appointment for Wednesday at the dealership. One of the key fobs has stopped working entirely, so maybe it was contributing to the situation. I am concerned, though, that if at least one fob is working, the dealership won't be able to troubleshoot the problem. If they can't find anything, I'll call roadside assistance and have it towed when it does this again.
My keys are kept in a separate part of my purse from my phone so I don't think interference is the issue.