If you're currently connected to the Slingbox with Slingplayer Desktop 2.0, it will provide you with the IP address of the computer that kicked you off. Otherwise, I don't believe there are any other logs that will provide you with the information you require. Probably, its easier to change the admin and guess password of your Slingbox.
Some months ago now I sent a bug report to Sling about a problem with the on screen remote. One day I was working on my computer with the TV on but muted next to my computer screen. The TV is attached to a set top cable box and all of a sudden I saw the screen change to an on demand pay-per-view pr0n channel - not yet purchased. I freaked not remembering in the heat of the moment (no pun intended) whether I had a password lock on pay-per-view and wondering what the heck was happening. I figured it must have something to do with the slingbox and I quickly pulled its power cord. I then changed my Sling passwords.
I called Sling and got connected to a support guy who indeed was testing the on screen remote with my SlingBox with no advance warning to me that he would be doing this. And he had hit some buttons that went to the offending screen and could not find a way out. And no, it was not because I have ever ordered such pay-per-view (not that there is anything wrong with that) as I never buy any pay-per-view unless I get a free movie code from my cable company - and they do not give them for pr0n. And I do as it turns out have a pay-per-view lock. And then it took the both of us some 10 minutes to get out of that offending screen. Even turning the set top box off and on and pushing every button we could think of did not work. I do not even remember now what we finally did to get out of that.
Anyway, somewhat of an amusing story about others using your SlinBox. SlingBox personnel should NOT be connecting to your box without your explicit permission. The tech guy said he figured no one would be home but I work at home. And thus I caught him.
BTW, the remote problem eventually got resolved. Some buttons critical to DVR content management had been impotent (ok, pun intended this time).