Why does a tire patch leak near the lip, and how to properly patch the flat?
The edges of patches tend to come unstuck because you are attaching a stiff flat patch to a curved surface. To avoid this, make sure that the vulcanizing solution covers the entire area of the patch, apply pressure to the entire patch while it is curing, and wait a sufficient amount of time before reinflating the tube.
And as others have commented, abrading the tube before patching does also help get a good seal. Sometimes you’ll get a secure patch without it, but your chances are much better if you do it.