The Microsoft tech support person I'd spoken to previously called me this morning, and wanted me to add these registry settings:
For 2013:
[ H K E Y _ C U R R E N T _ U S E R \ S o f t w a r e \ P o l i c i e s \ M i c r o s o f t \ O f f i c e \ 1 5 . 0 \ o u t l o o k \ R P C ]
" D i s a b l e R p c T c p F a l l b a c k " = d w o r d : 0 0 0 0 0 0 0 1
For 2010:
[ H K E Y _ C U R R E N T _ U S E R \ S o f t w a r e \ P o l i c i e s \ M i c r o s o f t \ O f f i c e \ 1 4 . 0 \ o u t l o o k \ R P C ]
" D i s a b l e R p c T c p F a l l b a c k " = d w o r d : 0 0 0 0 0 0 0 1
Of course, it didn't actually fix the problem, but he indicated that it might fix it for some people. May be worth a shot.
@JRG_MSFT
All of the suggestions in your response are the same things the tier 1 guys are having everyone try, and it doesn't work. And like someone else said, if it was a problem on our end, why would the connectivity come and go like that? Seems like it would just never work if it was a problem with the client, not just randomly connect for a while then disconnect.