Hi there,
I've been having this problem with oQueue since the last few versions, I think ever since 1.8.x (if I recall, 1.7.8 was ok).
I am NOT using Battle.net desktop client.
If I disable oQueue, the disconnects are gone.
I have currently 30 btag friends added, all except 1 added via oQ.
One other thing I noticed is I often get quite a large "time drift" discrepancy. It can get as much as 15+ minutes. Sometimes logging off and back in help, other times not.
I also noticed this getting a bigger problem in later versions. Sometimes it takes up to a minute (usually a few dozen seconds) for the addon to register when I put myself in a queue (or cancel it).
At least in my case, the culprit for disconnects is 100% oQ - if perhaps in union with another addon, can't say, but as I said, I only get the disconnects when I have oQ enabled.
Still, one of the best addons around, kudos to everyone involved.