I received a few requests for my full manuscript about six months ago. One agent told me that she liked the story, but one specific part at the end seemed a bit unrealistic to the situation. I thanked her for her time, said I was sorry it couldn't work out, and went off to go weep in my keyboard. A couple of days went by, and I started to think about what she said a little more. I realized that the issue she had with the ending could have been fixed with a few added sentences of explanation, or something of the like. It really think I could have made it work. I kicked myself for not realizing it sooner, and even though I've moved on from that novel (it never worked out), I still keep thinking about it.
So my question to you is:
Would it have been out of line to email the agent back with my suggested fixes? Or is a rejection on a full manuscript considered the end of the line?
I tried to convince myself that if the agent thought the manuscript would work with a few changes she would have said something, but I can't help wondering just the same.
It's the end of the line. Absent the phrase "revise and resend" or "fix this and send it back" or "if you fix this, I'll take another look" the agent has said No, thanks. In other words, absent a specific request to get in touch after revisions, don't.
Often I can point to one or two things that will help a manuscript improve and I try to give that info to writers when I'm passing on their work. The piece of information you're missing here though is this: that's not the only reason the ms is not right for me. There are a lot of good manuscripts out there that aren't right for me. A pass from me (or any agent) doesn't mean anything except it's not right for them.
Expand your query search. It's really easy to focus on the agent who wrote back, but you need to look for other agents because the right one won't know about you till you query her.