It's a trap...
The ONLY reason they don't want passwords changed regularly is so their database od cracked passwords doesn't have to be re-cracked every 30/40/... days.
Whilst I don't think CESG will be interested in ANYTHING I use/type/mail at my work (and have a far simpler way of accessing), I'd be *very* surprised if my personal addresses/accounts have not crossed their automated tracking: as Snowdon clarified they do try to watch *everything* on the interwebs after all!
The boredom of the content thereof is irrelevant: because my "stuff" is visible, they can hone in on drug dealers, terrorists and enemies of the state: we all know how "much" they use encryption and strong passwords eh? Right. Also, and more worryingly, they'll be able to home in on the genuine freedom fighters, oppressed peoples, press leakers, journalists and other folks validly trying to prevent their life/rights/privicy from being trampled.
I strongly believe we who know how owe it to everyone to work against "Big Brother". ENSURE that passwords are changed often enough to ensure they have to work for their intelligence, and can't snoop at will due to lazy password security. ENSURE that we implement adequate security on our own machines and gateways, and where possible onto those machines that we can influence.
And for those tempted to use pen a paper: DON'T. Get/make yourself a good password "system" (or a good app) and stick to it while changing important passwords regularly.