If I'm going to court for an eviction, do I lose my house because my ex-girlfriend pocketed the rent money that was automatically deposited into her account?

Unfortunately, one thing has nothing to do with the other in the eyes of the law. If your rent has not been paid, then the court will issue your landlord a "writ of possession". Once served, you must vacate your house. The fact is that your landlord is entitled to be paid per the terms of your lease; if not then they are entitled to re-possession of the rental premises, plus any back rent still owed.

However, that having been said, you can sue your ex-girlfriend. You can file suit against her in small claims court for the amount of the misappropriated rent and any costs/fees that you were forced to pay on account of the eviction. You will need to bring whatever documents, witnesses, etc. that you can has proof of your claim. Yet, if your girlfriend has no other money/assets collecting may be difficult (unless she has a job, then you could garnish her wages).