Maybe some fluke. Have you tried deleting this copy with
DeleteFile@CloudObject["https://www.wolframcloud.com/objects/9d51bc03-ccaa-4ee4-bb15-d65ca75d0b6c"]
And trying to re-deploy it?
CloudDeploy[
Manipulate[
Plot[{n!, 2^n, n^2, n Log[n], n, Log[n], 1}, {n, 0, 10^e},
PlotRange -> {{0, 10^e}, {0, 10^e}}, AspectRatio -> Automatic,
PlotLegends -> "Expressions",
PlotLabel -> "10^" <> ToString[e]], {{e, 1}, 0, 10}],
Permissions -> "Public"]
Part of it might be that the resulting Manipulate is slow. It is trying to plot on an exponential PlotRange after all.