If a court ruling in California awarded me sole custody on my daughter, how long is that good for? Does it expire?

The order is valid until modified by written agreement of the parties, or further Court order. An appeal would not be his route, he would just petition for a modification based on a change of circumstances which is a very broad concept and there are few limits on those filings; however, being there are few limits does not mean that there would be any changes to the orders.