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You have to make sure your rope is fully repaired before you can pick the flowers smile
I did the same thing. Laid my rope down and went after a hummingbird and couldn't figure out why I couldn't pick the fully bloomed flower.
Then I went back and put my villager on the rope again.
Initially, I thought maybe you had to repair it twice because I could have sworn I already put the villager on the rope to repair it.
I must have just missed because you only have to repair it once.

And thanks blinky and Becca! Didn't even think to put children on the flowers. Considering how much faster the children move, this makes a huge difference in how many tech points you can rack up!