Is the check engine light on?
If so, do you know what codes are stored?
This year Corolla has a known bad issue with the cars computer. Do you think you could look under the glove box dash(just above where your feet would be) and read the computers part #?
It will be something like 89661-02K20......could you reply back with what #'s you have?
I will keep check here.
This a common symptom of the computer going bad. There is a Service Bulletin EG042-07 and the computer is covered by warranty for 8yr/80,000miles. Have the Dealer replace it, they should have one in stock as we replace these on a weekly basis, and all should be well with the car running normally.