first, double check for some odd reason your scripts themselves arent disabled? (view the sidebar and then make sure they all got checks).. but i suppose if you see the sites connecting, then what is the last character you see in the [ ]'s next to the site name on the status bar.. is it "*" or "!" ?
next to that, theres no reason Bit Che would function normally and then all of a sudden stop working.. unless its getting interference from something else.. because none of the Bit Che code or its modules have changed. thus, maybe something has modified one of the dependencies, or even your tcp/ip stack, etc..
so... did you install any other new software? or even Windows Updates?
i'd start by looking at that, double check your firewall (which is it?)... oh, btw, does Updating Scripts work? how about Check for Updates? then we know Bit Che can access the internet fine... and we have some other funky problem =/
ps, what OS you running, and firewall software, etc?