At the bottom of the screen, above the tab bar, is a "Show All" button and another button which allows you to select a saved search. If you select a search from here then beorg will remember and show it again the next time you go to the Task tab even if beorg is restarted. However it doesn't currently support showing a specific saved search, rather than the last one. It sounds useful to do as you described, I'll have a think about if this can be implemented in a future update.
Don Morrison
Maybe there's a way to do this that I've not yet found, but assuming not:
It would be great to be able to configure beorg so that when first going to the TODO list an initial saved search is used. Granted, it's a little thing, just saving a few taps, but as it's such a frequent operation it would be most welcome.
Thanks!