What you are looking for is Greenshot:
- screen capturing software for Windows: √ just for that, yes – but also for OSX
- allows me to capture a defined region of my screen …: √ yes. Also full screen or a window
- … over and over again …: √ that's called "Capture last region"
- … by pressing hotkeys: √ shift+print
Screenshots of Greenshot (source: Greenshot; click image to enlarge)
As the screenshots show, you get some bonuses on top of that – e.g. hotkeys for other types of screenshots (window, full screen etc.). Also, once you created a screenshot, a popup menu will ask you what to do with it. For your screenshot sequences you'll probably chose "Save directly" (in which case it will be saved to your default/last location, using the program name and a timestamp as file name). But you can also copy it to the clipboard or even open it in an editor, e.g. for annotations and highlights.
Greenshot is completely free. Many companies have it installed on their desktops by default (in fact, almost any company I worked for here) – and I'm pretty much satisfied with it. Were it not preinstalled, I'd see to fix that gap (they even have a portable version – very useful in a company that doesn't let you install software). In short: I warmly recommend it!