Some thoughts, and likely force related - too light, so it pops out:
1. Some records can be different than others towards the end.
2. Check the tracking force (pressure on record) setting for your player & cartridge (e.g: 1.8g) - if you haven't yet make sure the tracking force is set properly - there are some youtube video's to watch.
- I suspect it might be too low so can pop out.
3. Make sure your anti-skating force is properly set (usually this should match tracking force). Mine is slightly higher.
Hope this helps, I suspect you've set the tracking or anti-skating force a bit too low so it pops out.