I used a little soapy water to find the leak. By inflating the tire then wetting it with soapy water, you can find the leak by looking for the bubbles. I thought at first that the old repair site might be leaking but it didn't take long to find the new leak. The bubbles were just churning out one after the other. Close inspection showed a tiny piece of metal, most likely a broken off barb tip from barbed wire. I couldn't grasp it to pull it out, so I pushed it through. Next I retrieved the tire repair kit from the workshop.
This kit is easy to use. It must be since even I can do it successfully! Thread a patch onto the tool, push it through the hole (the most difficult part of the job), rapidly jerk out the tool, and wallah.....fixed!
In this photo, the patch is the brown spot between the two tire knobs. I ran the ATV around the driveway once to seat the patch and make sure it wasn't leaking. Then I trimmed off the excess after I took this photo.
Learning to make basic repairs to equipment is important to a small homestead. By doing it myself, the equipment isn't out of service for very long. In this case, just 10 minutes. It also didn't cost me much. The kit was less than $5 and is good for three repairs.