Spinal stenosis epidural shots: how long does it take to see a difference and know it is working? They work for about an hour and then it's back

Several days. If it only lasts @ an hour it may be the numbing medicine in the shot . It takes the steroid several days to start reducing inflammation and pain.
Epidural Injections. Epidural injections are a common way of treating pain caused by stenosis (narrowing of the spinal canal due to bone spurs or disc protrusions). While these injections are often very beneficial for a high percentage of patients who receive them, it is very difficult to predict how effective they will be for a particular individual. In most cases, patients report improvement within 2-3 days.
Steroids & stenosis. Epidural steroids may be effective with mild central stenosis (mostly back pain) and perhaps somewhat more likely to be effective with foraminal stenosis (mostly pain below the knee) of fairly recent onset. However, if there is no sustained relief after an injection, there is no point in repeating as the adverse effects of steroids are cumulative.
Spinal stenosis. In general, epidural injections will provide relief for a few hours from the local anesthetic. Then the steroid component will start working within 12 hours and the improvement will be felt with 2-3 days. If the pain remains and you are limited in activities of daily living then it is likely that the stenosis is severe and the pain will not resolve without surgery. .
It varies. It's highly variable in patients I see from those who claim immediate relief to those who will tell that it takes several days up to a week to notice difference in pain. I am not a fan of these shots on the basis of many complaints for exactly what you're talking about where duration of effect is very short resulting in sooner returns with less positive effect.