PS insist to save as PSD

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible? 

Are you aware that the jpg’s compression-damage is cumulative, so by resaving jpgs the damage increases? 

@graverholt - As mentioned by @jane-e this is dependent on the state of the current file, not what you have done previously. Check colour mode, layers, channels and bit depth (from memory paths are OK).

And even for a JPEG file straight out of a device (phone, DSLR etc), if Photoshop can't read the compression and related metadata it will save in JPEG but ask what options to use. 

A script could force the issue for you if this was a constant issue for you.

@graverholt 

Are you opening a jpeg, working on it, and saving it? Or starting with a new document and saving? Or?

• Is your image 8-bit or larger?
• Does it have layers?
• Does it have paths?
• Is it flattened with a Background layer?

Does it have anything that a jpeg does not support? (You didn't say.) If yes, then Photoshop tries to save it as a PSD.

Jane