At what point does sleep deprivation become a problem?

As soon as it starts to impact your cognition. If your focus or attention go out the window, if you're sleepy during the day, and/or your reaction time and logic is slow. Sleep is important! Make time for it. Not sleeping for just a week can heavily impact your memory, learning and even produce hallucinations, if I remember correctly. And it takes time to make up those hours you've missed. They say it takes about a day to make up for every hour lost. That's why a 9-ish hour off jetlag can take up to two weeks to fix!