I generally find online polls a nuisance, but...
POLL
What's the greatest number of "go up, take a look/place gear, come down" laps you've taken on an onsight?
I think I did 6 or 7 on Ant's Line. On about #5 I got my hand sequence crossed up as I reversed the little layback up to the overhang, and had to work extra-extra hard to get back to the rest stance. Man, my abs ached for a couple days after that lead. But I got it!
I regularly go up and down to figure out a sequence. No idea what my record is, but it's probably around the same as your 6 or 7. Beyond that, unless it's a total no hands rest, I think you start getting into the realm of diminishing returns.
If I could add another spin to your question - how about the most times you've descended to the *ground* (or start of the pitch, for multi-pitch stuff) on an onsight?
I think the record for me is probably on Yellow Ridge in the Nears. I went up and down, trying the line DW describes, and then the one Swain describes. I couldn't find a way for either version to get me anywhere near the protection or difficulty level claimed in the two guidebooks we had. Then I finally tried something different (won't say what - don't want to spoil anyone else's onsight). And it turned out I actually did the line the way everyone else does!
There's a 5.10a in Eldo called Blind Faith. The FAist did the climb onsight, free solo. They went up and down many times, getting higher on the pitch each time, over several days, before committing and going all the way to the ledge. The scary part of the story is that the first 90% of the climb is waaaay easier than the last 10 feet.
GO