It clearly declares the author’s intent to give up asking in the face of being ignored, without any specific insult or derogatory behavior. Either not replying is fine with the recipient or it isn’t. If it’s rude to say “I won’t bother you again if you don’t reply”, what behavior would you replace that with that clearly indicates the outcome of choosing not to reply?

I encounter this frequently at work, where people either care deeply that they be heard, or do not — but regardless are unreliable at replying when asked to be heard the first time. Including “here’s my next course of action if non-reply” permits them to remain silently without being rude if they wish to.