Could Adam be the reason for losing Paradise?

I would first like to direct your attention to Sheryl's post, Was Paradise already Lost? Sheryl addresses the decision of Eve to work separately from Adam. I know that the bible shows Eve being tempted alone, and that the same event has to happen in Paradise Lost; but I cant help but feel that its somewhat Adam's fault. Adam gives in to Eves request and leaves her alone right after he is warned about Satan. This contradicts the idea of Eve getting directions from Adam, and instead portrays Eve as an authoritative figure, and Adam a bit submissive to her. 

Then after they both eat the fruit, Adam turns on Eve, blaming her for their actions:

Desire of wandering this unhappy morn

(I know not whence) possessed thee! We had then

Remained still happy, not as now despoiled

Of all our good, shamed, naked, miserable! (9.1136-9)

However, Adam was the one who allowed them to part that morning. So his decision to let Eve go on her own was a decision that put Eve in the position to make the decision to eat the fruit. Is Adam not supposed to have more reason? So would it not make sense for Adam to stay with Eve to be a source of reason and to prevent her from being tempted?

Yet it is still a common belief that Eve should be the one blamed for the fall because she was the one to take the fruit, eat it, and then feed it to Adam. It seems as though Adams lack of protection that day is overlooked to place the blame elsewhere. But I think that if Adam was with Eve, the blame would be placed equally on them- for they would both had been fooled. For now, I feel that responsibility rests on Adams shoulders, as he was the one to relinquish his role as Eve's protector that day. It was Adam who allowed Eve to wander on her own, when he knew of the increased dangers she could face.

Rebecca R.