So the other day near the end of my ride, I noticed that my rear tire had very low pressure (not flat, but maybe <20 psi). Because I was near the end, I decided to just pump it up with my hand pump. Of course, by the time I got back it was pretty low again, but it held some air. My rear tire was in need of replacement, so I decided to put on an old tire (very unworn, but not brand new. Of course, I forgot to replace the tube at first, so it lost pressure as well. And when I did replace the tube, all I had was my hand pump, so I probably only got it to 60 or 80 psi. But it held the pressure all night and through my next ride. After that ride, I finally had access to a floor pump, so I pumped it up to the usual 100-110 and left it overnight. I came back this morning, and the tire was basically flat. The real reason this seems odd to me is that it lasted 15 hours at a bit lower psi, but once I fill it to 110, it loses all its air in about 12 hours. I'm wondering if anyone has any suggestions as to what might be the problem, or how I might go about fixing this?