The problem apears to be a random holes opening up during the thermal stress
experienced during of soldering.  As several have already mentioned, small
holes in thick boards are prone to this failure, especially when the material
has a high "Z" axis expansion at soldering temperatures.  These material are
the epoxies with a Tg below 170oC.  Polyimides ot BT is suggested for this
application or some of the higher Tg epoxies may be used.

It does not sound if the allowance for a plated-shut hole is the problem as
any platiing solution entrapment takes a long time to work.  In the industry
many holes are not only plated shut but may also be filled with solder during
the fusing or HASL process and attempts to clear the hole so that the the
plug gage may be inserted is often disastorous to the board.

A microsection will often show the cause of failure and may also show that
the other holes that survived may be marginal for the product.  A repeat of
info from many studies is: (1) the thinner the platings in small holes the
more failures; (2) If the board is subjected to thermal solder it is best to
have it made from a material which has a Tg above or near the soldering
temperature; (3) deleting internal lands and using high resin
laminate/prepreg also will cause a higher CTE and increase chances of failure
in small holes in thick (above 0.04 inch) boards .

Phil Hinton
Hinton PWB Engineering 
hintpwb.com