It appears that on 64-bit Intel Macs, MacPAR deLuxe version 3.8 sometimes stops working, for no apparent reason. If this happens, the program just won't start up anymore. In some cases an error message is shown saying "The application par264 quit unexpectedly"; in other cases nothing seems to happen at all.
The problem is still under investigation, but so far I have never been able to reproduce it on my own 64-bit development machine.
For the time being, there is a solution in the form of a patch. To apply it, do the following:
Effectively, the patch disables the 64-bit component of the program, forcing it to run in 32-bit mode only. This might have a slight negative impact on the performance.