In a recent public statement posted on the Battlefield: Bad Company website, by the EA DICE development team; the recent connection (and online gameplay) issues that players are having is addressed and a promise of a fix is revealed.
"We are aware that some X360 players are having issues connecting to the Bad Company servers.
To all Bad Companions playing on Xbox:
We are aware that some X360 players are having issues connecting to the Bad Company servers.
We’ve been monitoring stats non-stop and are working with several partners to locate any possible flashpoints and eradicate any hostiles we encounter.
Until we are ready to implement a permanent fix, a possible workaround is to turn off your console for approx. 20 minutes before turning it back on and connecting again.
We apologise for the inconvenience to those of you who are experiencing this connection issue."