To put it simply, "quota" here means required quantity. In general, the word quota refers to an upper limit: "The government wants to set a quota for immigration", or a goal to reach: "Under the plan, private companies are legally required to fill a 3% quota with young employees."

"Quota" means "a required amount." For example, if everyone needs seven hours of sleep, then you could say "seven hours is your quota."

Amount.

A "quota" is an allowed amount. It is not a required amount. It is an allotment that you are permitted to have. "Your full quota of sleep" means the amount of sleep you are permitted to have. It does not mean the amount of sleep that you need. Hence your sentence means the same as: "If you don't get the full amount of sleep you are permitted to have, your work will begin to suffer."