I have a similar problem, and it seems to be erratic. Basically my PCs only show my Lumia's tabs when they feel like it, and I can't identify a particular trigger/connection error on the phone's part. When this happens, my phone will completely disappear as an option from IE, but it will reappear sometime later in the day. I doubt it is the PCs' problem because both PCs (laptop and tablet) will exclude my phone from the tab options at the same time, never one without the other.
On the other hand, my phone will always show my PCs' tabs in IE mobile.