I’m kind of in one of those “can’t look up the spelling of the world if you don’t know how to spell it” situations. :o
I’m not sure if this term is for Shakespeare’s protagonists, or specifically his lovers, but hopefully you might know that as well. At least knowing the word itself would make getting a decent definition a heck of a lot easier. 
You are not, by any chance, thinking of hamartia? That is not specifically Shakespearian (and does not actually refer to lovers), but it is classically defined (in English) as “tragic flaw.”
It is the Greek word meaning “misses the mark,” that was applied to the protagonists in Greek tragedies. Typically, the protagonist was a great person, capable of exercising power judiciously, displaying wisdom, and leading others well, but one who suffered a single flaw that caused them to career away from greatness to end in destruction. (The word hamartia also appears in early Christian writings where it is frequently translated (in English) as sin.)
Certainly, that “tragic flaw” is a component of Shakespeare’s works, as well. (E.g., Lear preferring the blandishments of his faithless daughters to the honesty of his faithful daughter.)
That was indeed the term I was looking for, and thank you for your clarification of the definition, as well.
Nice to know there are such cunning linguists aprowl.