What causes seemingly normal transactions to not be confirmed? I seem to be having an issue with transactions lately. Here is the most recent one. I paid 0.0004 BTC in fees, and I see there are quite a few inputs, but this seems like a normal transaction and should clear. However, I submitted it through a Multibit wallet about 15 hours ago and it has still not been included in a single block. Two other transactions I attempted recently have also been rejected, not even showing up in blockchain.info. What is the problem?

What, generically, is going wrong here and how can it be prevented?
Priority is an outdated concept and most miners don't use it anymore. Similarly, the standard fee is out of use.

Today, miners appear to be selecting transactions based on transaction fee per data size measured in [satoshi/byte].

Your transaction gave a fee of 0.4 mBTC and was 3471 bytes. This computes to 11.5 satoshi/byte. Currently, the predicted fee to get into the next block is 40+ satoshi/byte. Transactions with 11-20 satoshi per byte are predicted to have a 90% chance to be confirmed with a delay of 1-18 blocks.

If your MultiBit wallet is not up to a current version, you might experience better fee estimates by updating. A lot of wallet providers have vastly improved their fee estimations lately.