How many times can a single user poke another person on Facebook? Consider checking out this article: How to poke somebody that poked you on Facebook
How Many Times Can You Poke Someone?
The highest number of times you can poke someone on Facebook is dependent on how many times the poked person is willing to poke you back.
Mind you, you can't poke someone that have not poke you back that is, you can't poke one person twice. If the person decides to poke you back, you can poke again.