I've had three blind-reviewed academic articles published, and all have involved at least minor second R&Rs before being accepted.
But, largely due to wording I guess, I especially struggled with this question in one case recently. On the first R&R for this manuscript, I'd been asked to make fairly substantial revisions, including a significant reframing and focusing in on certain things the reviewers wanted to emphasize but felt were underdeveloped. I had done this, taking most of the (long!) period I was given for revisions, and then waited another fairly long time to hear back. The response was what gave me pause - even knowing that these things often require a second revision, and feeling very much that R&Rs represent a significant investment and interest on the part of the journal, the wording of the editor's message read as less than encouraging to me. It sort of said: "it's improved but still just not there and seems to have a way to go; we'll look at another revision, but of course we make no promises and considering how long its taking us, and how long its taking you, its fine if you'd rather withdraw it and try somewhere else."
I felt, at first, like the editor was basically telling me he didn't have much hope for the piece. But then my father, an academic himself well aquainted with both sides of the journal publishing process, became the first of several people to point out something obvious: it's their job to tell you if they don't want to publish it! Failing that, you have to read anything else as positive! If they had anything less than a continuing hope of publishing it, they would (or sure as hell should) say so, because it's to nobody's advantage to string you along. With a bit of renewed confidence from him and my very supportive writing group (and, yes, a good bit of "well it's gone this far I have nothing to lose by making the suggested changes and trying it one more time"), I spent another few weeks fixing it up and sent it back. Low and behold, I got an email just a few weeks later saying it had been accepted with no further changes at all.
Now I don't know entirely what to make of this particular situation, but I think the moral is nonetheless that further revisions are almost always a step forward (unless you seriously disagree with the direction the editors want you to take it of course) and indeed probably suggest that the journal is likely to ultimately publish it if you give them something close to what they want. In light of that, while I hear what Lawrence is saying above about not wanting to be stuck in peer review forever, if something has already gone through revisions once and come back for more, I think its almost certainly still going to be quicker to keep fighting through the current editorial gauntlet (at a presumably more desireable journal) than starting afresh somewhere new (and presumably less desirable). Or, at least, it worked for me.