I've never seen an application that stop my internet from working if itself hasn't access to it. But this happens with WinStep. I can switch/test this behavior with deny/allow the access Winstep in Kaspersky.

That sounds very strange. But I'm not wondering, if the software was last updated over a year ago.

So I think I have no choice to uninstall it, instead of buy it. I don't invest in software that has no support and is not maintained.

i think you'll find kaspersky is your problem and not winstep

Probably true, what chucky said.
I have no experience with Kaspersky, so I have no idea what paranoid way of virus "protection" they've come up with.
However, bear in mind that most applications that are launched through Winstep (or Nexus) are registered by Windows as "child processes" of Winstep. Therefore, Kaspersky, by not allowing Winstep to access the internet, *could* also be blocking all child processes as well. So you end up with, say, Firefox not having access to the internet, if you launch it from a dock shortcut.
That is not a problem of Winstep, it's how Windows works.
I don't know why you wouldn't want Winstep to access the internet, though. If it's blocked, none of its modules will work, like the weather module or the e-mail checker.

if skagon got it right and i think he just may have you'll want to go into you advanced setting for your firewall and check which components are and are not allowed accesses to the net and change the appropriate ones.