How many times a year can I enter Thailand on a 60-day entry permit stamp?

I enter Thailand weekly on a 60-day visa-exempt stamp. No issues

Q. how many times a year can we visit like that?

-> There is no written limit. However, approval of your entry is always at the discretion of the officer at the passport control desk upon your entry.

If your family will visit you only on holidays, it will not be a problem.

Q. I think I was told by someone you can only visit twice a year on this entry stamp?

-> That is old and incomplete information. There used to be the rule of the limit of two visa-exempt entries by land per calendar year. It has been lifted months ago. There has never been a limit on entries by air.