A New Dictionary

The humble thrush hardly seems a model of sturdiness, though it most probably accounts for the word.
Sturdy today means 'strong, robust, resolute'. About 600 years ago, however, in Middle English, it meant 'giddy or impetuous' - a nice case of amelioration once again; the links presumably were something like this: impetuous . . . reckless . . . violent . . . forceful . . . strong.
The word came into English from the Old French estourdi, 'stunned or dazed', from estourir, 'to stun'. And the way this word came about is probably as follows: there must have been a Vulgar Latin verb exturdire, which meant more or less 'to be stunned like a drunken thrush' - thrushes apparently having a tendency to get drunk by eating overripe grapes. The Latin roots of the word would have been ex-, 'completely', and turdus, 'a thrush'.

Taken from 'What's in a word' by John Kahn