[HerenIstarion]

When the Ring was cut off his hand at first, Sauron diminished, but the Ring was not destroed and he found some strengh to rebuild himself a housing body, and wasted another great amount of his inherent power in the effort.

It seems to me that the power left in his person after final rehousing was less that that of the Ring, and he could not preserve positive balance, some point at the scale, beneath which it was impossible to remain incarnate or perform incarnation, the balance convenient to preserve (or regain) bodily form, (the thing that he managed in the Akkalabeth and after the first loss of the Ring), if the Ring was destroyed.

Or, to put it other way round - when the Ring was cut off, he diminished and might have thought that to be the effect of the Ring-destruction. He managed to rebuild himself once again, but in that effort, he spent some more of his power, and after that last rebuilding the Ring-destruction became the deadly peril for him