Yes, debugging the server can cause the client to hang because the server does not send anymore. The client will hang as long as you single step. But that should normally not matter when you want to catch a certain event on the server.
We've meanwhile also looked into the send_skill_id functions and found indeed a potential problem. Under some circumstances, the id could be wrong. That can cause exactly the problem that you had.
This should not happen with the upcoming 8.10 version that's to be released in the next days for public beta test. I suggest that you wait for that version, and until then, use send_skill_to instead of send_skill_id. If the problem still happens in 8.10, please post again.