I have the exact problem!!!
I bought my canon optura 20 4 years ago at more than $900 and got the exact problem more than one year ago. I found that if turn it to play back mode and run the tape for a few minutes and then run the tape back, or just view the photos for a few minutes, and then turn to camera mode and it turns back to normal. But it is a pain to do this each time, especially when you want to shot something quickly but you have to repeat this stupid thing. And it always turns off automatically, even thought you want to keep it on to avoid this trouble.
I just found this forum today and sadly found that not only mine has this problem. This is definitely a product defect and Canon should recall this product. By the way, did anyone get any new feed back from Canon, or has repaired it? Thanks.