As far as I know latexmk automatically defines what to do when running it. So compile it several times that all references are correct.
However this takes a loooong time when I just want to check my table. Is there any way to disable this automatic behaviour and say that it just should run pdflatex once and then show the result?
In arara, for example, this is possible.
pdflatex -pdf texfile.tex
instead oflatexmk
.latexmk
is stll doing its thing. And to answer the OP's actual question, you can dolatexmk -e "$max_repeat=n" ...
wheren
is the maximum number of passes it makes before it gives up (the default is 5).