I've duplicated this on my system. Seems like an easy fix, if it is indeed a bug.
While running L4 (with an internet connection) , if I I deselect such options as "Logos Blog" or "Logos News" or "My Logos Messages" on the Customize Home Page menu, the changes are immediate and will remain active if the next time I run L4 I am online at the time. So far so good.
If I run L4 in off-line mode, no on-line content is retrieved from the server, and my homepage looks like it did previously. Again, as expected.
However, if I load L4 again -- this time connected to the internet -- all my options I had deselected are now selected again! Seems like this is a bug to me -- L4 should not reset my selections, but rather remember them.
I'm using 4.0a SR-3.