What could cause my 2001 BMW 525 to not start when it during heavy periods of rain?
Plug wires are suspect 1.
Coil over plug set-up so wires are out. With the engine running spray with water to try a duplicate. Really the first thing that should be done is a complete scan looking for something odd. Relying on a scan to show something on a GM could be considered folly but BMW has a much more developed internal test capability.
Thanks oldschool, the spray water is a good idea, probably ignition related, now how do I get the vcr to stop flashing 12:00? 
Your ignition control module should be in the firewall toward the passenger side. If water leaks into the recess where that module is located, it will shut you down and can destroy the ignition control module. Observe where the wires disappear through the insulation on the firewall, and next time the car fails to start, open it up and see if there is water in there around the control module. One reason that water can get in is if the drains in the air intake at the base of your windshield get plugged up so that intake fills with water and overflows down the firewall.
Thanks for the great advice I have taken it to the dealership today to get a diagnostic run as I had a similar problem last year and they told me it was the ignition module. Today they said the only thing that tested bad was the alternator I did not pay them to fix it as they wanted an arm and both legs for the repair. I purchased a new altenator with the intention that I could fix this myself for a reasonable price and since now the car does not restart once I turn it off after getting a jump I figured it made sense that it was the altenator. Would water getting into the ignition module cause the altenator to short?
It is rare for the alternator on these cars to fail. Did they say if it was failing to charge or if it had a bad diode?
Problems with the ignition control module would not affect the alternator.
BTW, I may have been wrong about the location of the ignition control module. That is where it is located on the 3 series, but I am not familiar with the 5 series.