I'm appalled at the perspective of middle class for you. If $500K is barely middle class, how would you classify a grad student? I suppose you were once a grad student too.
I'd consider "being able to save enough to continue a modest quality of life for retirement" a normal feature of what describes middle class life.
If you are living paycheck-to-paycheck you'll suffer when you hit old age or have a disabling condition that prevents you from working.