Once she leaves Canada, the application for the extension becomes invalid. Her return to Canada would result in a new entry (unless it falls into very specific categories) and new assessment by CBSA.
Anytime you apply for any type of extension be it work permit, visitor record, or even PR. You are in implied status/in processing, you lose this status as soon as you travel outside Canada and you will be treated as fresh newcomer if you try to re-enter Canada.
She is free to leave Canada anytime but once she re-enters, officer at the airport will do fresh assessment of her eligibility to enter Canada, if she is found to be living here long term on a visitor's visa, she could be refused entry to Canada and sent back.
Once she leaves you should send in a webform indicating that your mother has left Canada. As others have pointed out she is still a visitor in Canada so shouldn’t just be visiting her home country for a few weeks and returning to Canada.