My bet is Magento is not guilty here
Static files are cached by default by most modern browsers (you should play with configuration of the browser you use & see if you can disable that feature, or you can try browsing in incognito mode... although I am not sure that would download all static resources every page load, as you require)
Another possible reason, looking your comments, is some cache system in the server where your project is hosted. Most hosting providers use Nginx as web server for static files. If you inspect with your browser the concrete resource you want to download you'll find info, such Expires header (the time when your browser will download again that resource) or the Web Server serving that (maybe Nginx, or even Varnish...)
Considering all of this, a trick to get a 100% fresh version of your file would be trying to add some parameters when calling it (M2 does that https://docs.magento.com/m2/ce/user_guide/system/static-file-signature.html, so you should look for a similar approach in M1), or simply renaming the file
A workaround, if you can't work in a local environment (where you could control that Nginx / Varnish part...), could be placing your Javascript code in a Magento phtml template (which won't be cached if you have disabled Magento cache types) untill your work is done, and then move it to the right Javascript file