3 visits to Thailand this year would indicate to Immigration that you are no longer a tourist and I suspect that Immigration will require you to enter with a long term visa appropriate to the reason for your stay. If you attempt to enter on a visa exempt I suspect that you would be denyed entry.
You cannot renew a retirement visa. It expires at the end of its term. I suspect that prior to your visa expiring that you obtained an Extension of Stay based on being over 50 years of age. That is not a retirement visa.
For Australia, you really need a well prepared application. My has has had two approved tourist visas and I had no difficulty obtaining a tourist visa for my daughter.
As an American passport holder you can arrive in Thailand without having a visa. At the arrival airport the Immigration officer will give you (currently but planned to reduce at a future unknown date to 30 days) a 60 day visa exempt stamp in your passport.
Best to do in your home country because it has become almost impossible to open a bank account in Thailand unless you have a long term visa. And to get a retirement visa (or extension of stay based on being over 50 years) you need to show 800,000 Thai Baht in a Thai bank account.
If you get the 60 day visa exempt stamp and extend by a further 30 days at the Immigration office, Immigration class you as a tourist. If you then attempt to enter again on a visa exempt stamp, Immigration rightly consider that after on 90 day stay in the country that you are no longer a tourist but that you are attempting to live long term in the country. While there is no legal limit to the number of Visa exempt entries, once the Immigration officer believes that you are no longer visiting the country as a tourist he will deny you entry. If you have already stayed for 90 days on a visa exempt entry, then in future to guarantee entry into Thailand, you need to obtain a long term visa suitable to the reason for your stay.
You are contemplating Undertaking a process which is illegal and if found out by Innigration, you face possible imprisonment and certainly expulsion from the country and you query whether the process is normal. If you do not have sufficient funds to stay legally in the country go home.