hi!
I find it very annoying when my internet connection breaks down and kmail tries to fetch my mails that I get an error message for each mail account. I happen to have 9 accounts so that are quite a lot of message boxes to click.

Is there a solution?

I don't know whether that can be done. You can disable automatic mail checking from Settings -> Configure KMail -> Accounts -> Modify and uncheck "Enable interval mail checking" there.

I would have thought Solid was used to check to see if an internet connection was present. However, it seems that KMail hasn't yet been written to use Solid, probably because they will switch to Akonadi, who will have to handle it instead ( probably already does )