I got a puncture in my tube (size 700c x 23c, Kendra, came with bike) and applied a vulcanizing glue and patch, then checked it. Before reinstalling the tube, there was now a new leak right next to the patch, but the air is definitely not escaping from the lip of the patch, just very close to it.
So, I added another patch. Now the same thing happened again: a new small leak right near the patch but not from the lip of the patch.
I noticed these new leaks before reinstalling the tube, so the problem is not anything on the rim or in the tire.
I am relatively new at this so wanted to see if this has happened to others and what might be causing it.
Following the patch kit instructions, I applied pressure using the kit box from the center of the patch out. Would this potentially rip a new hole? Do I need to be very gentle with this step?