Hi Miss Plum,
I had posted a similar question a few weeks ago but hadn't picked up any response. So thank you for posting this question as I feel it very significant. I too am in this boat after a couple of R&R from agents and feedback from this kind group of authors. I consulted with a trad published author friend of mine along with two professional freelance editor friends of mine. All suggested waiting a couple of months before sending such a note asking whether the agent might like to review the new version instead of the old one. Otherwise, it may come across as a nudge, which I guess is usually reserved for when you receive an offer of representation or sufficient time has passed (i.e., 2-3 months for a partial, 4-6 months for a full seems to be a standard range).
Of course, the risk with this approach is that this increases the chance they have already read or started into the old version.
I do agree that honesty is the best course. I also feel that opening up and asking politely (as littlewritings shared) seems to work. For instance, after any personal rejection, I always politely ask for feedback and whether they might allow me to act on them. A couple have declined, a few have not responded, but three have agreed to a resubmit. One offered to take another look if I re-oriented my memoir towards the YA market and suggested some YA books for me to read up on. So I guess it goes back to the old axiom "it never hurts to ask (politely)." And, as I learned from a mentor many years ago, most people are willing to help if you humbly ask them for counsel.
Another observation I have made in my limited experience: it appears to spur some agents to action when you honestly share with them that you have been receiving attention/feedback from other agents. For example, I will ask them for their perspective on some feedback that other agents have provided. Again, a few have responded positively with their views.
So, getting back to the original question, I do plan to send newer versions after some more time has passed and just being upfront and saying, sorry, but this is now better. If you wish to stick with the original, please by all means do so. If somehow you have not gotten to my MS, then you have the option of a new one. Would you like to see it? I think it might be fine to do once. Of course, perhaps this gets me banished to the far corners of the query world by an agent or two, but I question whether they would do so if the MS resonates with them. And if they do, is this an agent I would really partner well with?
Not sure whether the more sage and experienced authors agree with any of my approaches.
Thank you again, Ms. Plum, for bringing up this pertinent point for many of us.
RCL