When you jump and place a fence beneath your player once you fall you will pass through the fence. After leaving it's hit-box you cannot re-enter the block.
Environment
Manufacturer: Dell
Model: Inspiron 5423
Processor: Intel(R) Core(TM)
i3-3217U CPU
1.80GHz 1.80 GHz
RAM: 6 GB
System Type: 64-bit OS
Java 7 Update 25
Duplicate of MC-11242
For security and stability reasons, I would strongly suggest you update your Java to the latest version (1.7.0_65): http://www.java.com/en/download/.
When using a 32-bit browser on a 64-bit operating system the automatic version detection will only show the 32-bit version of Java, the 64-bit version needs to be downloaded manually: http://www.java.com/en/download/manual.jsp.