I sent the previous message using the e-mail interface, and I see that rather than taking the signature I have defined on my Subscriptions page, ...
I'd expect both to appear. That is, I wouldn't expect Groups.io to detect your email sig and do anything like replace it.
which I do have the "use for e-mail posting" checkbox checked, ...
Interestingly, as a moderator of this group I don't see that you do:
Unless you've been changing the setting as a test, maybe what's buggy is the checkbox itself, or how it is displayed. Or something.
For Thomas I see neither checked, but he says he's been changing his so that might just be how he left it.
This message, by the way, is coming via the web interface again.