Sliding door handle/latch
Thanks for reaching out! The handle set you have can be replaced with the 82-030 Sliding Patio Door Handle Set or its keyed version, the 82-030A.
The issue you described sounds like an issue with the internal mortise lock in the door. Your looks like the 82-265 Multi-Point Mortise Lock. To confirm that this is the correct replacement be sure to carefully compare the dimensions below.
Keep in mind, your existing keeper may not be compatible, so you may need the 82-249 as well.
I'm happy to help! Please don't hesitate to reach out with any other hardware repair projects you might come across.
Have a great day!