When trading with villagers that have a low number of trades by default, those villagers can have all trades permanently locked. This occurs because there is no mechanism that refreshes the villager after every trade has become locked.

To reproduce:
1. Get a low trade number villager like Leatherworker or Fletcher (4 trades)
2. Trade until all trades are unlocked
3. Continue trading with villager the maximum amount for each trade
4. After some time (it took me ~10 minutes) you will get unlucky and trades will all lock

I believe that this can happen to other villagers but is much less likely due to higher number of trades.

Here is a link to a picture album showing that this is possible: http://imgur.com/a/QsvRy