Bill,
Like Eddie said. Also, when was the last time you flushed the brake fluid? I mean, completely replaced the fluid. If you push the pistons back into the calipers without opening the the bleed valve, you pushed the old contaminated fluid back into the brake system and ABS. Even if you bleed the brakes, you are only taking out any air, and there may not be any, but the brake fluid also has attracted moisture and that moisture is still in the line. The heat from the brakes turns the moisture to steam which is a compressable gas.
I think what you are feeling is the moisture in your brake fluid converting to steam as you apply the brakes and then you are compressing that steam which gives you the soft pedal at the end. I would recommend flushing all of the old brake fluid out and replacing it with fresh fluid. This is done just like bleeding brakes except you will constantly have to keep refilling the brake fluid reservoir as you flush out the old fluid. Never let the fluid in the master cylinder reservoir run empty or you will get air into your master cylinder and that can be hard to get out...You sometimes have to remove the master cylinder and bench bleed it.
...Rich
