I've not used omweather, but if any application is initiating a connection in the background without user interaction, it's violating the guidelines in the Maemo 5 developer guide.

The email client will check email periodically so long as there's an active internet connection. That's the design, that's the behaviour. If you want periodic checking, stay connected.

But you say you've got "connect automatically" checked. You still haven't confirmed that this does actually create a connection for you. If it doesn't (and accounting for the "search interval") you may have found a connectivity bug.
If you disconnect manually, then of course the email client isn't going to be able to check your mail. That's not a bug.