The timers that are even cheaper with the little red and green tabs that you pull out and stick in at the time you want them on & off are the worst. They fail when the tabs pop out & don't trip the switch. I found that out the hard way, lol.
That's exactly the kind that I use, with the green and red tabs. I've never had it fail like you describe, but I just find it real crappy because it's simply not accurate.
If I set it for 12 AM - 12 Noon, I don't want the timer to be shifting every damn day by a minute or two. I'm probably going to pick up a digital timer the next time that I happen to be at home depot.