“I can’t take another shift this week” isn’t letting the team down. Burning out and quitting next month is.

A limit stated in advance protects everyone who depends on you. Saying yes past what you have leaves you thinner each week until something gives, and the version of leaving that happens then is sudden and impossible to plan around. One declined shift is a small, manageable piece of information. A resignation in a month is not.

Say the no while it is still only a no, and be specific about what you can do instead. You do not owe a full account of your reasons. Managing your own supply is part of being reliable rather than the opposite of it.