The plot thickens....
I have used an ESR meter and found all tantalums and electrolytic capacitors to be in a good shape. A new bit of information arose from using the VME riser card. While the board was on the riser, sticking out of the chassis, I could NEVER get it to fail, after many many power cycles. So I decided it might be temperature related, and I put an antistatic bag over the board for 10 minutes to let it warm up a bit. I noticed that the supply current dropped from 100 mA to 99 mA very steadily while the bag was on, and as soon I removed it, I started rising again. Long story short, the board temperature increased to 92 Fahrenheit in those 10 minutes (87F before), and a voila on the next power cycle it failed. Interestingly, the only component that changed temperature in failed state besides the 3.3V regulator, was the ADSP-21065L DSP (normally 90 F, in failed state 109 F). I power cycled one more time, the board booted and the ADSP went back to 91F temperature. Thats where I'm at now.....
T