The "fresh eyes once" was what Susan Hawk told her client, Marcie Colleen. And it's so true! They'll lose the ability to critique your work well if you go back and forth with them too many times, just like any crit partner.
Once I get an idea I really like, I send the idea to my agent to get her feedback. Is it worth pursuing? I don't want to spend weeks, months, YEARS on a story she doesn't think has a compelling enough hook. Sometimes I send her the first few lines, sometimes just a title, sometimes a premise.
I won't send her a first draft. I'll go through at least two rounds of crits and revisions first. And then I get impatient and send it to her, LOL.
That being said, one of the things I asked her before I signed was how often she expected something from me. She said it was up to me--she would work at my pace. At the time I signed, in 2010, I still had one child at home 3 days a week and didn't think I would be able to write that often. But I suppose signing with my agent made me find the time!
During our 3 years together she's had something out on submission 90% of the time. I haven't hit a manuscript dry spell yet (although I certainly have hit selling dry spells, LOL). I've surprised myself in being more prolific than I originally imagined.