Objectivists quote Rand:
"The basic principle of altruism is that man has no right to exist for his own sake, that service to others is the only justification of his existence, and that self-sacrifice is his highest moral duty, virtue, and value."
I can see how they believe this leads to self destruction. Indeed the altruist acts with "selfless devotion to the welfare of others" according to my dictionary, a definition not at odds with Rand's description.
The slef-immolation quote is at odds with the dictionary definition. The one you cite now is not descriptive of Randian ethics. Rand did not merely say: As you give of yourself, make sure you have enough left to survive; she said, Do not make virtue out of altruism at any level.
In order to do something for the welfare of others one has to have something positive to give. Albert Schweitzer did not self-immolate, he built a hospital and lived to be 90.