My bitcoind runs 24/7, and has 4 specific other nodes that I run, which it connects to... This wallet is only used for Satoshidice, so no other TX's (aside from the one I funded the wallet with) exist.
Neither a rescan, nor a re-download of the blockchain resolved the issue.
I'm currently rebuilding the wallet by exporting all the private keys from it and re-importing them 1-by-1 into a new wallet... it will take a few days to run, since there are ~2100 private keys and it averages 45 seconds per key to import. I'll let you know how it works out.
That will work, but it would be a lot quicker to just remove the bad transactions from your wallet using PyWallet.
Why don't you try exporting the keys you used in the faulty transactions first and importing them into your new wallet - then you'll see that the bets have been paid out, and that it's just bad transactions in your wallet that prevent you from seeing them.