Why Does the JIT Continually Recompile the Same Method?

A Stack Overflow user noticed frequent recompilations, even after a substantial JVM uptime, and couldn't find an explanation based on the common knowledge on JIT compilers.

We know that the Java JIT compiler compiles and recompiles methods based on usage statistics. As a method gets called repeatedly, interpretation moves to JIT compilation. More frequent calls can trigger recompilation with a higher optimization level. Despite of that theoretically simple optimization chain, the actual compilation invocations visualized with -XX:+PrintCompilation can look like they're not following that strategy at all.