How many battles did the Spartans lose?

Answer 1

Two battles actually, one to Thebes, and then again to the Romans when they conquered all of Greece.

Another view:

The Spartans lost quite a few battles, from early struggles in the Peloponnese, Messenia when they had to call in the Athenians to help them recover, Sphacteria after which they called a truce with Athens, several sea battles, through to the defeat at Corinth, then against Thebes at Leuctra, and as a waning power, losses during the 2nd Century BCE after which Sparta became militarily impotent.