Can a US citizen re-enter Thailand after a week in Singapore if they initially entered for 40 days?

Hi, I have been to Thailand 6 times this year, I fly home for a while and come back for 60 days exempt visitor visa stamped at Thailand airport, no questions ever asked, it seems to me a visa is not needed if you fly out and re enter

Short answer is YES

You get 60 days visa-free every time you enter Thailand

Yes

If you come here without having bought a visa at a thai consulate in your country before you get here, you'll get stamped in FREE for 60 days on what's called a "visa exempt entry" and you can extend that entry one time at the immigration office for 1900baht

When you leave that stamp cancels.

So if you go to singapore for a week then come back to thailand you'd get in on a NEW 60 day free entry stamp (and could extend that for 30 days at the immigration office too if you wanted to for 1900baht)