One downside of a 64 bit application...
The answer is easy: Your 64 bit application can use terabytes of memory. No limits basicly. Okay, if physical memory is low, the system will use the hard disc to extend memory. Swap files grow over hours and at some point the hard disc is full. Guess what happens if both memory and harddisc are full?
Well, the system will crash with an out of memory error.
By the way, a 32 bit application will stop or crash once it wants to allocate more than 3.5 GB of memory.