Actually, neutral ending for FT shows them as pretty big empire, with endless expansion.
And in FO3 it is said "There's also a small detachment in
Chicago, but they're off the radar. Gone rogue. Long story."
CHICAGO! One city, not entire 2 commonwealths or 12 states (!) with lot of cities under them.
Also, after end of FT midwestern BoS changed it capital to Vault 0... so look at that map.
And take into account, that Caesar's Legion hasn't any fights with mid BoS over some cities etc. They just caught few BoS people from east, confirming that by 2281 they exist FAR east from Denver.
So everything confirms that mid BoS lost it capital, and therefore, judging from FO3 words, by 2281 mid BoS exist ONLY in Chicago, while having problems with manpower and everything (they're small, not empire like during F:T)... so they're pretty dying as a faction since BoS expedition to DC or rather few decades before this event.