Can I continue to renew my 6-month tourist visa in Thailand if I own property?

I don't know where you got that the 6 month METV is for property owners, because whether you own property here or not makes no difference on whether you can get one of those visas from the thai consulate in your country.

BE that as it may..

You need to understand that VISAS are sold by thai consulates in other countries which are run by the Ministry of Foreign Affairs office.

AND

You get stamped in to the country by thai immigration officers which are a division of the Royal Thai Police.

Just because a consulate sold you a visa does not mean that the immigration officers have to let you enter the country on it. :O

People with valid visas in their passports have been denied entry to the country at the discretion of the immigration officer who was stamping them in.

Now with that being said I know people on their 4th or 5th back-2-back 6 month METV from the same consulate who have had no problems getting into the country on them.

BUT

no one can say for certain if you will skate right in or if you will be taken aside and questioned. All you can do is be prepared with the proof of funds (20K baht or the equivalent in CASH), proof of onward travel and proof of lodging.. Have those and hope for the best...