Why is it difficult to mix helium and nitrogen gases?

It's true. Special equipment and a long time is required to mix helium and nitrogen. According to one study, a mixture of 2.7% He, 93.3% N$_2$ at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://pubs.acs.org/doi/abs/10.1021/je60005a002. The helium repeatedly slid from one end of the cylinder to the other. The authors overcame this difficulty by devising a mixing mechanism internal to the cylinders.

The molecular weight of helium is 4.02, and density is .1786 kg/m^3 at standard temperature and pressure. For nitrogen, molecular weight is 28.02, and density is 1.2506 kg/m^3. Here's a table of molecular weight and density for various gases: http://www.engineeringtoolbox.com/gas-density-d_158.html.

Helium doesn't mix easily with nitrogen because of the great difference in their densities. But once mixed, the gas molecules are close together and they move around quite a bit with kinetic energy so they stay mixed and don't separate out into layers.