Once I protect a document it will not let me send for signatures. How can I send a password protected document for signatures?
That is true you can't send a password protected using "Send for Signature" option.
Also, you may check this: How to encrypt your documents using Adobe Sign wherein you can password protect your file.
But you can access Send for Signature service via browser https://cloud.acrobat.com/sendforsignature then you will be able to see the option mentioned in the KB
Let us know if you have further questions.