Configure Browser Switchboard with any default browser other than MicroB. Restart the device. Open a link from an application or a desktop widget; the link should open in the default browser you configured. Open MicroB by using the Web menu entry (you don't need to change the default browser setting or restart the device). Open a link from an application or a desktop widget; the link should open in MicroB. Close all the MicroB browser windows. Open a link from an application or a desktop widget; the link should open in the default browser you configured. Open MicroB by using the Web menu entry (it should come up).
Please let me know whether this works consistently now or not, and whether or not you notice any other inconsistent or strange behaviors. If anything doesn't work as expected along the way, please let me know; if you can, open an xterm, run "killall browser-switchboard; browser-switchboard", go through the sequence of steps, and then provide the output that browser-switchboard produces in the terminal when reporting your problem.
Also, please report any problems you have with MicroB losing bookmarks, history, or settings when it's closed; a change to more heavy-handed measures for killing MicroB in a previous release may have introduced such bugs.