Hi Opal
Let me say in advance that I have left my reading glasses at home today. Without them, I am seriously challenged in terms of reading the screen! Please therefore forgive the typos with which this reply will be litlered.
The requirement is that the Sponsor (either you or your sister) must have Permanent Residence before the application is made. The sponsor also has to have been settled in Oz for a "reasonable period." The legislation itself does not define "reasonable period." However the Policy manuals say that two years would be the norm in most cases.
With regard to repeated tourist visas, it is not as clear cut as it might seem. Since the introduction of the Contributory Parent visa scheme in 2003, the Oz Govt has become quite hostile to the idea of allowing Parents to use repeated long stay visitors as an alternative to applying for a CP visa. Their argument is that a tourist visa cannot be used as a means of "living" in Oz.
They are more cautious with the over 70s than with parents under that age. You have not said how old your mother is. If she is 70 or over, she would have to get her own GP to complete a simple form of medical certificate for her. Please see here:
http://www.australia.org.uk/lhlh/health.html
I reckon that they take heed of what the doctor has said in deciding what to permit. My mother is now 86. After she turned about 75, DIMA started restricting her to six months at a time actually in Oz, but they made the visa valid for travel to Oz with8in 12 months of the date of its grant, and valid for multiple travel.
The effect of that was that for about 10 years, Mum would travel to Oz from the UK. After 6 months in Oz, she went to somewhere like Bali for a couple of weeks (from Perth.) Then back to Oz for another 6 months. Then back to the UK and she usually spent about 2 or 3 months here before starting the cycle again.
It was a rickety sort of arrangement but heck. If the family wants to be together, you don't moan about rickets, do you?!!
Cheers
Gill