Have you tried doing the ps | grep ? You'll find that it doesn't do what you expect, and will always be true:

slightly:~/desktop oneiros$ ps -aux |grep PROGRAM
oneiros    840   0.0  0.0    27352    424  p1  S+    9:57PM   0:00.00 
+grep PROGRAM
[download]

What you want is called a 'watchdog' program (sometimes called 'wxdog', depending on the application)

Oh -- and while doesn't take an else ... you need an if inside the while ... and you'll want to sleep so you don't suck down all of the CPU.

But the better solution is to find why the problem is dying.