One of the main problems with the design of Fallschimhager is that they have not real weakness.
Other high damage infantry units are either only good at one range like Shocktroops being only good at close range or Obersoldaten being good at long range or have a lack of anti tank weapons like Paratroopers, Obersoldaten or Shock troops.
The easiest solution to give Fallschimjager a direct counter would be to remove the Panzerfaust. Now they can still be really good at all ranges like they are now, but still directly counterable if unsupported.
Weakness? I am sure they are the most squishy elite infantry in coh2. Without the snare, they even can't retreat safely from a M20 or a M3.