Hi,
H&C doesn't offer any Stays or status so you'll want to continue to apply for extensions to her visitor's status.
You'll want to build a good presentation and look at the online manual for the "factors" that are considered by the decision-maker. Interestingly, or perhaps not, H&C's in its earliest incarnation in the 1970s were commonly accessed by people who had a parent visiting and where the other parent passed away. Here's the link and it's the factors that should be your focus.
http://overseastudent.ca/migratetocanada/IMMGuide/CICManual/ip/ip05-eng.pdf
If you'll entertain some thoughts, these applications are now frequently submitted by unsuccessful refugee claimants who have removal orders and these are given priority when they have accompanying PRRA applications. I mention this because you could wait a couple of years for a decision. H&Cs are a "living" application, meaning that you can submit updated information to the application while it moves lugubriously through the inventory of cases that they process.
So, perhaps your mom attends language classes, or volunteers somewhere within the community - these are important additions for the officer to entertain when they assess they application. Should it take so long that your mother has to leave then the application will still be decided no matter where she may be.
In my experience on this site there are lots of judgments made and some dig for details, but H&Cs have always had a better than 50% approval rate. Statistics are always more interesting beneath the surface numbers and failed refugee claimants who have been here for years and have children tend to have greater success. But these are decisions where there is as broad a level of discretion as you'll find within Canada's immigration system, so hope burns brightly for a well constructed application.
Good luck.