It could be either the valve or the booster; they're about equally suspect.
The hoses to the valve should not affect the ability to retain vacuum. The
valve is easy enough to check by pulling it out and giving it The Kiss of
Test. You should be able to blow through it from the booster end to the hose
end but not the other way. Now wipe that silly black ring off your lips. :-)

If the valve tests okay you are probably in the market for a new booster.
(The "probably" is from doubts whether pushrod adjustment can cause your
symptoms - you can check the adjustment by following the link below.)
Replacement is a medium DIY project with tight spaces, and wrecking yards
are the most affordable source (I paid $75 US to a they-pull-it yard for the
last one I did.) If you have to replace it, and you go the DIY route, check
http://tegger.com/hondafaq/mastercylinderreplace/adjustment.html for pushrod
adjustment info.

Mike

it should retain vacuum.  as mike says, test & replace accordingly.