When is it inappropriate to use systematic random sampling?

It is inappropriate to use systematic random sampling when your population has a periodic or cyclic order. This could result in only including individuals with a specific characteristic (e.g., age) in your sample.

Systematic sampling example: Unrepresentative sample
Your list of employees alternates between men, women, and nonbinary people. You select every third individual, which means you’re only selecting nonbinary people. This wouldn’t be a representative sample because the sample doesn’t contain any people who identify as men or women, whereas they make up most of the population.