Need to say that I rename those directories again to reconstruct stuck state of bitcoin core. Then run bitcoin-qt -reindex and this resolve problem too. So this is much easier way.

I had same problem.
Out of sync for few hours, then ten, then 40... Restarts and walk through proxy doesn't help. Eight connections were present and adding another nodes from https://en.bitcoin.it/wiki/Fallback_Nodes has no effect, "Network Traffic" tab in Debug Window doesn't show any serious activity.
Then I check data directory and found debug.log. There was interesting moment:

...
2014-05-28 20:53:03 receive version message: /Satoshi:0.8.6/: version 70001, blocks=303083, us=xxx.xxx.xxx.xxx:123, them=yyy.yyy.yyy.yyy:8333, peer=0.0.0.0:0
2014-05-28 20:53:04 ERROR: Proxy error: connection refused
2014-05-28 20:53:04 SOCKS5 connecting seed.bitcoinstats.com
2014-05-28 20:53:05 CheckForkWarningConditions: Warning: Large valid fork found
  forking the chain at height 302787 (000000000000000063db9b526e9cbe0cec7053157df6ea0f0ee895addc355b26)
  lasting to height 303083 (0000000000000000378f60f49b076dc6de665a3fd6eba18313ded3c61df65737).
Chain state database corruption likely.
2014-05-28 20:53:05 ProcessBlock: ACCEPTED
...


So I close bitcoin-qt, rename blocks and chainstate directories (to make illusion for bitcoin-qt that we have no local copy of blockchain), download boostrap.dat in this directory and next start of bitcoin-qt synchronize from file and then from network without problems and still ok.